JRA3: STREGA - TASK M4
Technical Report on Q measurements at room temperature
First year report (04/2004, 04/2005)
Leading group: IGR, U. Glasgow (19)
Abstract
This task has as its objective the measurement of the mechanical loss, optical loss and index of refraction of dielectric coatings of the type necessary for use in the mirrors for advanced gravitational wave detectors. Here we report on the results of recent work carried to study the mechanical and optical properties of low loss dielectric mirror coatings.
Introduction
All current interferometric gravitational wave detectors use suspended test masses to which ion-beam-sputtered dielectric multi-layer coatings are applied to form ultra-high quality mirrors. The mechanical losses of coatings currently available would result in a level of thermal displacement noise expected to be a significant limit to the performance of future ‘advanced’ gravitational wave detectors. The optical power incident on the coatings may be of the order of 100’s of kW, thus the optical absorption of these coatings must be of a low enough level to avoid significant thermally induced distortions of the interferometer mirrors. To ensure that future detectors reach desired levels of sensitivity and operate robustly it is essential that both the optical and mechanical loss of dielectric mirror coatings be quantified and, where possible, minimised.
The work over the first year of this project has been targeted at several tasks.
(1)The study of the mechanical loss of coatings formed from alternating multi-layers of SiO2/Ta2O5
(2)The study of the loss factors of single layers of the above coating materials
(3)The study of the mechanical loss of alternative coating materials such as Al2O3
(4)The study of the optical absorption of coatings formed from the above materials.
Studies of the intrinsic dissipation of coating materials of SiO2, Ta2O5 and Al2O3
An ongoing programme of research on mechanical losses of coatings at the University of Glasgow, working in collaboration with colleagues in the LIGO Scientific Collaboration and at LMA Lyon forms the basis of the first part of the work reported here. This programme of work showed previously that mechanical dissipation appeared to be predominantly associated with the Ta2O5component of the coatings [1]. High reflectivity dielectric coatings can also be formed from alternating layers of Al2O3and Ta2O5and SiO2and Al2O3respectively. The mechanical dissipation of these coatings is thus of considerable interest. We summarise here the results of measurements, carried out in collaboration with LSC colleagues, of the mechanical dissipation of ion-beam-sputtered coatings of Al2O3/Ta2O5, and SiO2/Al2O3, and compare the results with those obtained previously for SiO2/Ta2O5coatings. These results are to be submitted for publication, thus we present a summary only, and refer to the publication for fuller discussion.
If the intrinsic loss of a test mass substrate,f0)s, and the loss of a coating, f0)c, applied to the substrate are the only sources of dissipation in the system then the total mechanical loss, f0)cs, at a resonant frequency, f0, of a coated sample, can be written as
where Uc/Usis the ratio of the strain energy stored in the coating to that stored in the substrate. The strain energy ratio associated with each resonant mode of a sample can be found using finite element analysis (FEA). f0)sand f0)cs,can be experimentally measured.The experimental setup used to measure the mechanical dissipation of the coated and uncoated substrates studied here was that described in detail in [2].
In brief, measurements were made of the mechanical dissipation of coated and uncoated substrates. Two sets of disc-shaped samples were studied. The first set were each 7.62cm in diameter by 2.54cm thick and the second set were each 7.62cm in diameter by 0.25cm thick. Measurements were made of the mechanical dissipation of a number of modes of each sample. The resonant frequencies studied of the thin samples were between 2 kHz and 6 kHz while those of the thick sample were in the frequency range from 20kHz to 72kHz. The coatings studied include those discussed in [2] with the addition of coatings containing Al2O3as one of the layer materials. The complete set of coatings studied is given in table 1. Coatings 1,2 and 3 were fabricated by LMA, 4 and 6 by MLD Technologies (MLD) [3] and 5 by Waveprecision (WP) [4]
Table 1. Summary of coatings studied. All coatings were applied to fused silica substrates.
From the experimental measurements, and FE models, it was thus possible to obtain values forf0)c for each coating.
Our recent work [5] and that of our colleagues [6] has shown that dissipation due to thermoelastic damping, th(f), may contribute to measured coating loss. This type of damping arises from the coating and substrate having different thermo-mechanical properties. We may express the total coating loss as
f)c = th(f) + residual(f)
where residual(f) is the residual loss of the coating, which is potentially due to the intrinsic dissipation of the coating materials [7]. For a given coating th(f) depends on the fundamental thermo-mechanical properties of the coating and may thus be calculated analytically.
By calculating th(f) we thus were able to obtain values for residual(f) for each coating studied, and by knowing the fraction of each material present in a multi-layer coating we were able to obtain values for the residual dissipation of the individual coating materials in the multi-layers.
Figure 1: (a) Residual dissipation of the SiO2 and Ta2O5components of the coatings
(b) Residual dissipation as shown in (a) but with the addition of data for Al2O3.
Figure 1 shows the results of our evaluation of the residual mechanical dissipation of the SiO2, Ta2O5and Al2O3 material present in the coatings indicating that the dissipation is predominantly associated with theTa2O5 material and that the level and frequency dependence of the residual dissipation of Al2O3lies between that of SiO2and that of Ta2O5.
In particular we find
silica(f) = (0.2 +/- 0.5) ×10−4+ (2.8 +/- 0.8) ×10−9 f
tantala(f) = (5.2 +/- 0.4) ×10−4+ (−0.08 +/- 1.01) ×10−9 f
and we find the residual loss of the Al2O3 component of the coating to be
alumina(f) = (2.6 +/-0.2) ×10−4+ (1.1 +/-0.5) ×10−9 f
for the MLD coating, and
alumina(f) = (1.8 +/- 0.5) ×10−4+ (1.6 +/-1.2) ×10−9 f
for the coating from Wave Precision.
SiO2/ Al2O3coating
Typical high-reflectivity dielectric mirror coatings are formed from alternating layers of high and low index materials. The coatings studied so far use Ta2O5as the high index material (n = 2.03), with either SiO2(n = 1.45) or Al2O3(n = 1.65) being used as the low index material. Given that our studies suggest that individually Al2O3and SiO2both have low levels of mechanical dissipation, the mechanical dissipation of a SiO2/Al2O3multi-layer coating is of interest as it may form a coating combination having overall low mechanical dissipation.
However it should be noted that the small difference between the refractive indices of SiO2and Al2O3means that many more layers are required to achieve a high reflectance coating than is the case for a SiO2/Ta2O5coating. To achieve approximately 15 ppm transmission for a SiO2 /Al2O3coating 43 high-low index pairs are required as opposed to 17 pairs for the same transmission using a SiO2/Ta2O5 coating. For convenience, measurements were made here on a 30 layer SiO2 /Al2O3coating manufactured by MLD. As before the corrected thermoelastic loss for this coating was calculated and subtracted from the experimental loss to leave the residual loss. The residual losses for SiO2 and Al2O3 (from the MLD sample) calculated earlier were used to predict a level for the residual loss for the SiO2/Al2O3coating for each mode. These losses are plotted in figure 2 along with the residual losses obtained from our experimental measurements of the 30 layer SiO2/Al2O3coating and agree well.
These results can now be used to calculate the level of thermal noise associated with each type of coating at a frequency in the bandwidth of a ground based gravitational wave detector.
Our thermal noise calculations, presented in detail in [8] suggest that a SiO2/Ta2O5coating is currently the best choice for a fused silica substrate while a SiO2/Ta2O5or SiO2/Al2O3coating would be appear to be the best option for a sapphire test mass. Our results and analyses are all consistent with the residual coating dissipation being mostly due to the Ta2O5in the coatings. If this residual dissipation can be reduced to a level where thermoelastic dissipation becomes the dominant loss mechanism an Al2O3/Ta2O5coating would be the best choice for a sapphire substrate.
Figure 2: Comparison of predicted residual loss for a SiO2/Al2O3 coating compared with measured values.
To confirm the results of the studies using multi-layer coatings the mechanical losses of single layers of SiO2 and Ta2O5were investigated. The residual coating losses for the single layers were found to be
= (0.3 +/- 0.6) x 10-4 + (-2.1 +/- 1.3) x 10-9 ffor SiO2
= (7.0 +/- 2.1) x 10-4 + (6.7 +/- 4.4) x 10-9 ffor Ta2O5
It can be seen that these are in reasonable agreement with the results obtained from multi-layer coatings. It should be noted that the single layer Ta2O5coating had ‘cracks’ visible to the eye. The non-optimal structure of the material of this layer may have contributed to the higher loss of this material compared to that obtained from the multi-layer measurements.
Experiments aimed at reducing the dissipation of Ta2O5are ongoing, and results suggest that this may be achieved as a result of adding to the Ta2O5a small percentage of TiO2[9]. In particular the residual coating loss for a single layer of Ta2O5 doped with a small amount of TiO2 was found to be
= (2.2 +/- 1.1) x 10-4 + (1.6 +/- 2.3) x 10-9 f(doped Ta2O5)
Development of ‘membrane’ system to study single layers of coating materials
In order to allow rapid measurement of the mechanical loss factors of single layers of coating materials at the coating site a facility has been developed in the Perugia INFN laboratory and transferred to the CNRS-LMA laboratory of Lyon, where the coatings are produced and tested. This measurement system is designed to emphasis the effect of the coating dissipation on the measured dissipation of a coated sample by maximising the ratio between the surface where the coating is applied and the volume of the substrate. The best way was to apply the coating to a membrane of SUPRASIL 311 fused silica of dimensions 104 µm 5 mm 45 mm.
The membrane is attached to a stainless steel clamp, as shown in figure 3 (a) and inserted into a vacuum system, shown in figure 3 (b), and excited using an electrostatic actuator. In this way it is possible to excite many modes of the membrane, investigating the losses at different frequencies. Special care has been devoted to the clamp to reduce the excess dissipation in it; i.e. the clamp is polished after the insertion of the membrane, to have a net separation line between the membrane and the clamp. In addition care was taken to ensure that dissipation due to gas damping and recoil losses were of a negligible level.
The sensing of the resonant modes of the membrane when installed in the facility makes use of a Michelson interferometer, in which one of the two end mirrors is formed by a silica membrane, and the other arm is realized through the reflecting face of the common beam splitter. The interferometer should be kept on the grey fringe, where the output of the Michelson is linear with respect to a variation of the differential arm length. The light exiting from the interferometer is sensed using a photodiode and the ring-down of the sample, after the excitation, is digitalized through a system based on LabView.
Figure 3:(a) Clamping system for the membrane and (b) measurement bench at LMA for recording the measuring sample dissipation
A typical ringdown is shown in figure 4. The lower resonant frequency of the slab is about 60 Hz, and a so low value is important to access the dissipation of the coating in a frequency range very crucial for the thermal noise in future gravitational wave detectors.
Figure 4 : Data showing the ringdown of the amplitude of a fused silica membrane.
The envelope of the ring-down is calculated taking the modulus of the analytic signal f(t)+iH{f(t)}, where H{f(t)} is the Hilbert transform of f(t), and fitting it with an exponential to extract the total loss angle. The result of such a process on the sample of the figure 4 is shown in figure 5
Figure 5 Fit to the envelope of the ringdown of the amplitude of a silica membrane.
The angular coefficient of the fit is directly related to the of the oscillator through the simple formula
where f is the frequency of the resonant mode under study. The loss of the uncoated membrane uncoated was measured to evaluate the dissipation of the system consisting of the clamp and substrate:
where, e represents the excess losses (clamping, surface, …). Then, without removing the clamping system, the membrane is coated with a mono-layer of Ta2O5 and the mechanical loss of the coated membrane is then measured again. We may then write
The measured for a series of measurements was found to be uncoated = 9.46 x 10-6 andcoated=2.73 x 10-5.
To evaluate the effect of the coating and determine the loss angle of the Ta2O5, it is necessary to model the strain energy stored in the bulk of the membrane, Uvolume, and in the coating, Usurf. This was performed using an ANSYS finite element model in the Firenze INFN laboratory. This energy ratio, along with the measured loss values, may then be used with the equation above to calculate the coating loss angle. This was found to be
Ta2O5 =0.0021
This is higher than the results discussed earlier and studies of the reasons for the difference in these results are ongoing.
Studies of Optical Absorption
Since the delivery of the first set of the mirrors for the VIRGO gravitational wave detector in 2002, the quality of the dielectric coatings produced by LMA has been improved. Indeed, no systematic optimisation of the new large coater had been carried out at that time. Today, the absorption level, for example, has been improved from 0.7 ppm (value of the large VIRGO mirrors) to about routinely 0.5 ppm. Figures 6 and 7 show one of our best results: about 0.3 ppm absorption on a 1 inch high reflectivity (HL)19HLL mirror. H and L are respectively Ta2O5 and SiO2 quarter wavelength layers. The measurement was made at room temperature.
Among all the metrology tools used at LMA, the absorption bench is one of the most critical: the low absorption levels reached by our mirrors and the specifications for the future mirrors (about 0.1ppm) require a very high sensitivity.
The sensitivity for the absorption measurement on one point of a mirror is sufficient (0.02ppm). Nevertheless, it is necessary to record a map of the absorption on the whole surface of the mirror, in order to measure possible absorption variations. Unfortunately, the sensitivity for an absorption map was about 0.12 ppm (see figure 6). After some modification on the absorption bench (reduction of the noise induced by the motors of the translation stages, improvement of the pump laser power density, the signal processing,…) we now reach a sensitivity of about 0.03 ppm for absorption maps (see figure 7). Of course, this sensitivity is only reached with very low loss coatings.
Figure 6: Absorption map of a 1 inch HR mirror before modification of the absorption bench
Figure 7: Absorption map of the same mirror after modification of the absorption bench
Another improvement of the absorption bench has been made in order to be able to record absorption maps of mirrors having a curve shape or a wedge. Up to now, during a mapping, a curve or a wedge induced a deflection of the probe laser which was not proportional to absorption, generating an error in the measurement (see for example figure8 showing the absorption map of a VIRGO Recycling Mirror we coated last year, VRM03, which has a radius of curvature of 4.5 m). Obviously, the upper and the lower parts of the map are wrong, because the probe laser was deviated away from the quadrant detector.
Figure 8: Absorption map of VRM03 mirror before modification of the absorption bench
In order to overcome this problem, the quadrant detector has been fixed on a motorized mount with servo-control of its motion. Thanks to this modification, it is now possible to map the absorption of any mirror, whatever the shape of the substrate (see figure 9).
Figure 9: Absorption map of VRM03 mirror after modification of the absorption bench
A preliminary study on a new high index material, Al2O3 (alumina), has just started. As discussed above measurements of mechanical loss indicate that Al2O3 layers should have lower mechanical dissipation that than Ta2O5 layers. Within a separately funded contract with the LIGO project, a (doped Ta2O5/Al2O3)15 mirror has been deposited in the large VIRGO coater at LMA, on a thick (1”) sapphire substrate of 3” diameter. For the Al2O3 layer, a pure (99.999% purity) aluminum target was used. Unfortunately, the (doped Ta2O5/Al2O3)15 mirror has a high absorption level. Furthermore, this absorption is increased after annealing (see figure 10). This phenomenon may be due to a diffusion process between doped Ta2O5 and Al2O3. This phenomenon is less acuteif Ta2O5 is not doped. For example, a (Ta2O5/Al2O3)10 Ta2O5/(Al2O3)2 mirror absorbs only 430 ppm after coating, and 750 ppm after a 600°C annealing.
In order to reduce diffusion, a thin layer of silica (50Ǻ gives the best result) is deposited between each layer of Ta2O5 and Al2O3. In fact it is known that there is no diffusion process between silica and Al2O3. For example, a (Al2O3/SiO2)15 mirror (run C04094) gives an absorption of 55 ppm which perfectly corresponds to the simulated value, considering the measured extinction coefficients: k(Al2O3) = 6.10-6 and k(SiO2) = 8.10-8.
Figure 10: Absorption versus annealing temperature
The (doped Ta2O5/thin SiO2/Al2O3)15 mirror (run C040100) gives better results (see table 2) than run C04091 without silica barrier. Its absorption is around 70ppm (close to the simulated value with measured extinction coefficients) and the diffusion is 4ppm. This 3 inch diameter, 1 inch thick mirror has been delivered to the University of Glasgow, for mechanical quality factor measurement, during the last Ilias meeting on coatings at Lyon.
Substrate / N° Run / Centering (nm) / Absorption (ppm) / Absorptionsimulated / Diffusion
(ppm) / Transmission
(ppm)
µGO / C0410011 / 1063 / 69 / 100
Thick Al2O3 / C0410021 / 1069 / 70 / 100 / 4 / 3220
Table 2 Measured and simulated absorption for Al2O3/Ta2O5 coatings with doped Ta2O5