Current status of the loss measurements and loss

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Current status of the loss measurements and loss analysis 1 Mechanical loss measurements of

Current status of the loss measurements and loss analysis 1 Mechanical loss measurements of bulk and cantilever samples D. Heinert, C. Schwarz and P. Seidel Institute of Solid State Physics, University of Jena, 1 st March 2010 Heinert et al. 01. 03. 2010

bulk measurements cantilever measurements Current status of the loss measurements and loss analysis 2

bulk measurements cantilever measurements Current status of the loss measurements and loss analysis 2 outline I bulk measurements of mechanical loss • measurement setup • silicon - thermoelastic damping - Akhieser damping - interstitial oxygen • Ca. F 2 - defect damping II cantilever measurements of mechanical loss • measurement setup • silica Heinert et al. 01. 03. 2010

bulk measurements cantilever measurements Current status of the loss measurements and loss analysis 3

bulk measurements cantilever measurements Current status of the loss measurements and loss analysis 3 thermal noise in a conventional end mirror • thermal noise calculations by R. Nawrodt 300 K Ø 500 mm x 300 mm, (111)) HR stack (silica/tantala) 18 K • coating and bulk Brownian as limiting noise sources necessity of understanding underlying loss mechanisms systematic minimization of losses Heinert et al. 01. 03. 2010

bulk measurements experimental setup silicon cantilever measurements calcium fluoride Current status of the loss

bulk measurements experimental setup silicon cantilever measurements calcium fluoride Current status of the loss measurements and loss analysis 4 Mechanical loss measurements in silicon • silicon as proposed material for a 3 rd generation GWD many parameters to choose: elongation x/x 0 • measurements in Jena: resonant measurement of mechanical loss over T and frequency free decay - geometry - working temperature - doping - crystal orientation - surface treatment -… excitation resonant mode shape Heinert et al. time t/τ 01. 03. 2010

bulk measurements experimental setup silicon cantilever measurements calcium fluoride Current status of the loss

bulk measurements experimental setup silicon cantilever measurements calcium fluoride Current status of the loss measurements and loss analysis 5 measuring setup for bulk materials cryostat probe chamber (Ø 300 mm x 500 mm) labtour: 17: 00 Heinert et al. 01. 03. 2010

bulk measurements experimental setup silicon cantilever measurements calcium fluoride Current status of the loss

bulk measurements experimental setup silicon cantilever measurements calcium fluoride Current status of the loss measurements and loss analysis 6 Loss measurements in bulk silicon • own sample (Ø 76. 2 mm x 12 mm, (100)) • thermoelastic damping: • mode shape dependent FE analysis of TED is partly dominating the measured loss spectrum Heinert et al. 01. 03. 2010

bulk measurements experimental setup silicon cantilever measurements calcium fluoride Current status of the loss

bulk measurements experimental setup silicon cantilever measurements calcium fluoride Current status of the loss measurements and loss analysis 7 TED in bulk silicon samples • thin samples are partially limited by TED at low temperatures • we want to obtain new remaining loss processes • simulation of TED for different substrate thicknesses (Ø 76. 2 mm x h, (100)) • comparison of fundamental drum use bigger substrates to minimize TED Heinert et al. 01. 03. 2010

bulk measurements experimental setup silicon cantilever measurements calcium fluoride Current status of the loss

bulk measurements experimental setup silicon cantilever measurements calcium fluoride Current status of the loss measurements and loss analysis 8 Loss measurements in bulk silicon • Mc. Guigan‘s loss measurement 1978 (Ø 10. 6 cm x 22. 9 cm, (111)) • occurence of 2 loss peaks T=115 K: Bordoni-type relaxation but crystal is „dislocation-free“ T=13 K: corresponding energy levels in B peak with the same energy encountered in ultrasonic absorption measurements of boron-doped silicon Heinert et al. 01. 03. 2010

bulk measurements experimental setup silicon cantilever measurements calcium fluoride Current status of the loss

bulk measurements experimental setup silicon cantilever measurements calcium fluoride Current status of the loss measurements and loss analysis 9 Loss measurements in bulk silicon • own measurements on big samples a) Ø 76. 2 mm x 75 mm (100) b) Ø 76. 2 mm x 75 mm (111) c) Ø 110 mm x 200 mm (111) our measurements show no loss peak • possible explanation: difference in growth process large difference in the density of oxygen impurities our samples: floating zone crystals low oxygen density Mc. Guigan: Czochralski crystals high oxygen density Heinert et al. 01. 03. 2010

bulk measurements experimental setup silicon cantilever measurements calcium fluoride Current status of the loss

bulk measurements experimental setup silicon cantilever measurements calcium fluoride Current status of the loss measurements and loss analysis 10 oxygen interstitials in crystalline silicon • geometry of interstitial oxygen in silicon is well known - O is covalently bonded to Si - numbers 1 to 6 show equivalent defect positions defect induced mechanical loss possible • mechanical strain changes defect potential redistribution of defects Further investigation neccessary -1 - -2 - [Borghesi et al. , (1995) Oxygen precipitation in silicon] Heinert et al. 01. 03. 2010 -1 - -2 -

experimental setup bulk measurements silicon cantilever measurements calcium fluoride Current status of the loss

experimental setup bulk measurements silicon cantilever measurements calcium fluoride Current status of the loss measurements and loss analysis 11 Defects in loss measurements • defect occur as Debyepeaks in the frequency spectrum • temperature influences the relaxation time (Arrhenius law) • frequency dependence for the temperature of maximum loss (Arrhenius plot) Heinert et al. 01. 03. 2010

bulk measurements experimental setup silicon cantilever measurements calcium fluoride Current status of the loss

bulk measurements experimental setup silicon cantilever measurements calcium fluoride Current status of the loss measurements and loss analysis 12 Mechanical loss measurement as a spectroscopy method • well known quartz losses as reference for this purpose (Ø 76. 2 mm x 12 mm, z-cut) • Electromigration identifies alkali atoms to cause loss peaks [JJ Martin 1984] • correlation with dielectric loss spectrum result: activation energy (50 … 200 me. V) Heinert et al. 01. 03. 2010

experimental setup bulk measurements silicon cantilever measurements calcium fluoride Current status of the loss

experimental setup bulk measurements silicon cantilever measurements calcium fluoride Current status of the loss measurements and loss analysis 13 Damping mechanism due to phonons – Akhieser damping • principle requirements for mechanical loss a) at least two states b) interaction process between strain and energy of the states c) redistribution processes to equilibrium increase of entropy • phonon spectrum satisfies these conditions [Akhieser 1939] a) dispersion relation shows different eigenstates b) strain (acoustic wave) leads to frequency change - Grüneisenparameter c) collisions between phonons as redistribution process Heinert et al. 01. 03. 2010

experimental setup bulk measurements silicon cantilever measurements calcium fluoride Current status of the loss

experimental setup bulk measurements silicon cantilever measurements calcium fluoride Current status of the loss measurements and loss analysis 14 simple model of Akhieser damping • [Bömmel and Dransfeld, 1960] • model with two kinds of phonon branches a) branches with =0 b) residual branches with the same result: is characteristic time for establishing equilibrium time between phonon collisions • approach via transport theory of heat conduction Heinert et al. 01. 03. 2010

bulk measurements experimental setup silicon cantilever measurements calcium fluoride Current status of the loss

bulk measurements experimental setup silicon cantilever measurements calcium fluoride Current status of the loss measurements and loss analysis 15 Akhieser losses in silicon • substrate: Si (100), (Ø 76. 2 mm x 12 mm) [Touloukian] thermal conductivity depends on material and geometry • influence of dopants • especially at T<10 K great differences Heinert et al. 01. 03. 2010

bulk measurements experimental setup silicon cantilever measurements calcium fluoride Current status of the loss

bulk measurements experimental setup silicon cantilever measurements calcium fluoride Current status of the loss measurements and loss analysis 16 measurements on thermal conductivity • huge variety of thermal properties in silicon • own measurement on sample material allows detailed determination new smaller cryostate • first test measurements on silicon: Heinert et al. 01. 03. 2010

bulk measurements experimental setup silicon cantilever measurements calcium fluoride Current status of the loss

bulk measurements experimental setup silicon cantilever measurements calcium fluoride Current status of the loss measurements and loss analysis 17 Loss measurements in calcium fluoride • monocrystalline Ca. F 2 (Ø 75 mm x 75 mm, (111)) TED does not affect our measurements defect peak at 25 K peak at high temperatures due to setup Heinert et al. 01. 03. 2010

bulk measurements experimental setup silicon cantilever measurements calcium fluoride Current status of the loss

bulk measurements experimental setup silicon cantilever measurements calcium fluoride Current status of the loss measurements and loss analysis 18 Loss measurements in calcium fluoride • Arrheniusplot • measured temperature behaviour of the defect peak at low temperature Heinert et al. 01. 03. 2010

experimental setup bulk measurements silicon cantilever measurements calcium fluoride Current status of the loss

experimental setup bulk measurements silicon cantilever measurements calcium fluoride Current status of the loss measurements and loss analysis 19 Loss measurements in calcium fluoride • defect energy of observed loss peak EA = (10. 0± 1. 0) me. V relaxation constant τ0 = (3. 2± 0. 1) 10 -7 s • typical activation energies in Ca. F 2 energies > 1 e. V • color centres • polarization measurements at low temperatures („thermal depolarization“) [P. W. M. Jacobs, 1980] activation energies: 300 … 500 me. V (alkali impurities) oxygen impurity: Heinert et al. 01. 03. 2010 470 me. V

bulk measurements cantilever measurements Current status of the loss measurements and loss analysis 20

bulk measurements cantilever measurements Current status of the loss measurements and loss analysis 20 Loss measurements on coating materials • mirrors in a GWD need optical coatings additional loss sources • to maximize the effect of the coating on the measured loss we use coated cantilevers • mechanical loss of the compound • coating loss as difference between coated and uncoated cantilever Heinert et al. 01. 03. 2010

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bulk measurements cantilever measurements Current status of the loss measurements and loss analysis 21 Loss measurements on coating materials • we used silicon cantilevers as substrate material • experimental setup clamping structure capacitive excitation optical readout via splitted photodiode Heinert et al. 01. 03. 2010

bulk measurements cantilever measurements Current status of the loss measurements and loss analysis 22

bulk measurements cantilever measurements Current status of the loss measurements and loss analysis 22 Loss measurements on coating materials • silica coating on silicon cantilever • measuring strategy: 1. loss of uncoated cantilever 2. loss of coated cantilever loss peak at low temperatures Heinert et al. 01. 03. 2010

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bulk measurements cantilever measurements Current status of the loss measurements and loss analysis 23 Loss measurements on coating materials • new cantilever design • robust design (flexure protected by stable frame) easy to handle Heinert et al. 01. 03. 2010

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bulk measurements cantilever measurements Current status of the loss measurements and loss analysis 24 conclusions • low mechanical loss measurements in Jena possible (Qmax=6 x 108 on silicon) • measurements on silicon, crystalline quartz, calcium fluoride encounter of new defect peaks (spectroscopy) • thermoelastic damping well understood • simple model for damping due to phonons own measurement setup for thermal conductivity • cantilever measurements on coating materials outlook • investigation of doped silicon • new material: sapphire Heinert et al. 01. 03. 2010