Mechanical loss measurements of bulk and cantilever samples

Mechanical loss measurements of bulk and cantilever samples D. Heinert, C. Schwarz and P. Seidel Institute of Solid State Physics, University of Jena Jena, 1st March 2010

bulk measurements cantilever measurements outline I bulk measurements of mechanical loss • measurement setup • silicon - thermoelastic damping - Akhieser damping - interstitial oxygen • CaF2 - defect damping II cantilever measurements of mechanical loss • measurement setup • silica

bulk measurements cantilever measurements thermal noise in a conventional end mirror Ø 500 mm x 300 mm, (111)) • thermal noise calculations by R. Nawrodt HR stack (silica/tantala) 18 K 300 K • coating and bulk Brownian as limiting noise sources  necessity of understanding underlying loss mechanisms  systematic minimization of losses

experimental setup bulk measurements silicon cantilever measurements calcium fluoride Mechanical loss measurements in silicon • silicon as proposed material for a 3rd generation GWD  many parameters to choose: • geometry • working temperature • doping • crystal orientation • surface treatment • … • measurements in Jena: • resonant measurement of mechanical loss over • T and frequency free decay elongation x/x0 excitation resonant mode shape time t/τ

labtour: 17:00 experimental setup bulk measurements measuring setup for bulk materials silicon cantilever measurements calcium fluoride cryostat probe chamber (Ø 300 mm x 500 mm)

experimental setup bulk measurements silicon Loss measurements in bulk silicon cantilever measurements calcium fluoride • own sample (Ø 76.2 mm x 12 mm, (100)) • thermoelastic damping: • mode shape dependent FE analysis • of TED  TED is partly dominating the measured loss spectrum evtl. Diagramm

experimental setup bulk measurements silicon TED in bulk silicon samples cantilever measurements calcium fluoride • 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

experimental setup bulk measurements silicon Loss measurements in bulk silicon cantilever measurements calcium fluoride • McGuigan‘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

experimental setup bulk measurements silicon Loss measurements in bulk silicon cantilever measurements calcium fluoride • own measurements on big samples a) Ø 76.2 mm x 75mm (100)  our measurements show no loss peak b) Ø 76.2 mm x 75mm (111) c) Ø 110 mm x 200 mm (111) • possible explanation: difference in growth process  large difference in the density of oxygen impurities our samples: floating zone crystals low oxygen density McGuigan: Czochralski crystals high oxygen density

Further investigation neccessary experimental setup bulk measurements silicon oxygen interstitials in crystalline silicon cantilever measurements calcium fluoride • 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 -1- -2- -1- -2- [Borghesi et al., (1995) Oxygen precipitation in silicon]

experimental setup bulk measurements silicon Defects in loss measurements cantilever measurements calcium fluoride • 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)

experimental setup bulk measurements silicon Mechanical loss measurement as a spectroscopy method cantilever measurements calcium fluoride • 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 meV)

- Grüneisenparameter experimental setup bulk measurements silicon Damping mechanism due to phonons – Akhieser damping cantilever measurements calcium fluoride • 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 c) collisions between phonons as redistribution process

experimental setup bulk measurements silicon cantilever measurements calcium fluoride simple model of Akhieser damping • [Bömmel and Dransfeld, 1960] • model with two kinds of phonon branches • branches with =0 • residual branches with the same  result: is characteristic time for establishing equilibrium  time between phonon collisions • approach via transport theory of heat conduction

experimental setup bulk measurements silicon Akhieser losses in silicon cantilever measurements calcium fluoride • substrate: Si (100), (Ø76.2mm x 12mm) [Touloukian]  thermal conductivity depends on material and geometry • influence of dopants • especially at T<10K • great differences

experimental setup bulk measurements silicon measurements on thermal conductivity cantilever measurements calcium fluoride • huge variety of thermal properties in silicon • own measurement on sample material allows • detailed determination  new smaller cryostate • first test measurements on silicon:

experimental setup bulk measurements Loss measurements in calcium fluoride silicon cantilever measurements calcium fluoride • monocrystalline CaF2 (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

experimental setup bulk measurements Loss measurements in calcium fluoride silicon cantilever measurements calcium fluoride • Arrheniusplot • measured temperature behaviour of the • defect peak at low temperature

experimental setup bulk measurements Loss measurements in calcium fluoride silicon cantilever measurements calcium fluoride • defect energy of observed loss peak EA = (10.0±1.0) meV τ0 = (3.2±0.1) 10-7 s relaxation constant • typical activation energies in CaF2 energies > 1 eV • color centres • polarization measurements at low temperatures • („thermal depolarization“) [P.W.M. Jacobs, 1980] activation energies: 300 … 500 meV (alkali impurities) oxygen impurity: 470 meV

bulk measurements Loss measurements on coating materials cantilever measurements • 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

bulk measurements Loss measurements on coating materials cantilever measurements • we used silicon cantilevers as • substrate material • experimental setup clamping structure capacitive excitation optical readout via splitted photodiode

bulk measurements Loss measurements on coating materials cantilever measurements • silica coating on silicon cantilever • measuring strategy: 1. loss of uncoated cantilever 2. loss of coated cantilever  loss peak at low temperatures Wellenleiterbeschichtung

bulk measurements Loss measurements on coating materials cantilever measurements • new cantilever design • robust design • (flexure protected by • stable frame)  easy to handle

bulk measurements conclusions cantilever measurements • 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

Mechanical loss measurements of bulk and cantilever samples