Thermal noise and material issues for ET

Nawrodt 05/2010

Thermal noise and material issues for ET

Ronny NawrodtMatt Abernathy, Nicola Beveridge, Alan Cumming, Liam Cunningham, Giles

Hammond, Daniel Heinert, Jim Hough, Iain Martin, Peter Murray, Stuart Reid, Sheila Rowan, Christian Schwarz, Paul Seidel, Marielle van Veggel

GWADW2010 Meeting, Kyoto 20/05/2010

Institut für Festkörperphysik, Friedrich-Schiller-Universität JenaSonderforschungsbereich Transregio 7 „Gravitationswellenastronomie“

Institute for Gravitational Research, University of GlasgowEinstein Telescope Design Study, WP2 „Suspension“

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Overview

• Motivation

• Material Properties– thermal properties– mechanical properties

• Thermal Noise Issues for ET

• Summary

GWADW2010 Kyoto/Japan #2/54

Nawrodt 05/2010

Motivation

• ET will need a radical change in the materials in order to achieve the sensitivity goals:

– suspensions,– test mass materials,– coatings,– optical materials

• Additionally, going towards cryogenics temperatures will dramatically change material properties additional degree of freedom.

• The new material has to be compared to the best optical material currently available at room temperture!


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Material Properties – Thermal Conductivity in Crystals

GWADW2010 Kyoto/Japan

• typically 3 zones:

– higher temperatures: TC is limited by phonon-phonon scattering– lower temperatures: mean free path of phonons increases,

scattering at impurities becomes important

– high purity samples: at very low temperatures the sample geometry becomes important (scattering of phonons at the sample surface limitation of TC)

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Material Properties – Thermal conductivity of Silicon

experimental results (double-log scale!):

“recommended curve”(< 1014 cm-3 boron, approx.1 mg B in 1 t Si)

increasing impurity concentration (scatteringof phonons on impurities)

smaller structures + impurities(~ 1/L term)see Callaway 1961 or Casimir 1938

[Touloukian]


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• in high purity silicon the different silicon isotopes take the role as scatter centers (-> impurities)

• natural Si has 3 stable isotopes:– 92% Si-28– 5% Si-29– 3% Si-30

• they cause small local changes in the lattice due to their different atom masses effect is small

• however, concentration is very large compared to typical impurity concentrations (ppm range)



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• it is possible to enrich/purify silicon

• isotopic pure silicon shows a much larger thermal conductivity in the peak region compared to standard semiconductor grade silicon

• 99.8% Si-28:TC ~ 10x larger

• disadvantage:price ~ 1000 US$/gsemiconductor grade ~ 500 US$/kg

[Ruf et al., Solid State Comm. 115 (2000)]



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Mechanical Properties – Mechanical Loss of Materials

•


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Mechanical Properties – Surface loss

• sudden change of chemistry at the surface end of periodicity of crystal lattice remaining defect in perfect single crystals

• it was shown that the surface loss can be influenced by proper treatments (heating, passivation, etc.)

• however, most of these changes are not stable and the surface loss gets back to the initial level after hours


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Mechanical Properties – Impurities

• imperfection in crystals can change their states (moving, rotation, …)

• example: crystalline quartz (SiO2)

modelled as double well potential


view along the c-axis

OSi

E

ener

gy

position

21

TkE

0Be

“Debye-peak”

thermally activated transition

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Mechanical Properties – Impurities in Silicon

• doping concentration is variable lowest possible value will used

• most serious impurity in Si is oxygen from the growing process (electronically not active nearly no support from

semiconductor industry!)• two growing processes:

from melt from solidCzochralski-process Floating-Zone-process

O-concentration: 1018 cm-3 O-concentration: 1014 cm-3

max. dia. in some years max. dia. in some years~ 45 … 50 cm ~ 30 … 35 cm


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Mechanical Properties – Phonon-Phonon-Interaction

• fundamental process in crystalline solids cannot be avoided• two mechanisms:

– high temperatures / high frequenciesdirect interaction of one phonon with another one

(Landau-Rumer-process)

– low temperatures / low frequencies

elastic mode (low frequency phonon) changes the lattice change of the equlibrium distribution of phonons

redistribution needs energy loss

(Akhiezer-process)


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Mechanical Properties – Mechanical loss in solids


crystalline quartz silicon

impurities could be indentifiedto be alkaline ions from thegrowing process

origin of most of the peaks unclear(blue – oxygen in silicon)

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Mechanical Properties – Mechanical loss in solids


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Thermal Noise – Bulk Material


• Thermo-elastic noise:

• Brownian thermal noise:

32222/5

222BITM

TE wfC1Tk4)T,f(S

[Liu, Thorne 2000])T,f(S'C)T,f(S ITMTE

2FTM

FTMTE

[Braginsky 1999]

)T,f(Yw

1f

Tk2)T,f(S substrate

2

2/3BITM

X

[Liu, Thorne 2000]

)T,f(SC)T,f(S ITMX

2FTM

FTMX [Liu, Thorne 2000, Bondu, Hello, Vinet 1998]

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Thermal Noise - Coating


• Thermo-elastic noise:

• Brownian thermal noise:

[Harry et al. 2002]

''2),( ||22 Y

YYY

Ywd

fTkTfS B

x

[Braginsky, Fejer et al. 2004]

)(g1C

Cwd

fTk8)T,f(S

2~2

sS

FS22

2B

TE

2

AVGSS

SFS

S2~

1EE)21(

11

1C2C

FF

F

F isinhRicoshisinh

i1Im)(g

2SS

2FF

2

F CCRandd

note: for the coating Brownian noise the substrate‘s Young‘s modulus is important

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Thermal Noise – Crystal Orientation


[Wortman, Evans, J. Appl. Phys. 36 (1965)]

Selection of the crystal orientation for low noise performance:

)T,f(Yw

1f

Tk2)T,f(S substrate

2

2/3B

X

[e.g. Liu, Thorne 2000]

2 extreme values for theYoung’s moduli of Si:

Ymin = 130 GPa for Si(100)Ymax = 188 GPa for Si(111)

e.g. bulk Brownian noise:

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Thermal Noise - Overview


100

101

102

103

104

10-24

10-22

10-20

10-18

frequency [Hz]th

erm

al n

oise

[m/

Hz]

bulk Brownianbulk TEcoating Browniancoating TEcoating TRtotal

20 K

100

101

102

103

104

10-24

10-22

10-20

10-18

frequency [Hz]

ther

mal

noi

se [m

/ H

z]


300 K

Si(111) test mass, dia. 50 cm, thickness 30 cm, HR stack (20 doublets, Ta2O5:TiO2, SiO2)

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Thermal Noise – Temperature Dependence


0 50 100 150 200 250 300-0.5

0

0.5

1

1.5

2

2.5

3x 10

-6

temperature [K]

CTE

[1/K

]

100

101

102

103

104

10-24

10-22

10-20

10-18

frequency [Hz]

ther

mal

noi

se [m

/ H

z]


5 K

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0 50 100 150 200 250 300-0.5

0

0.5

1

1.5

2

2.5

3x 10

-6

temperature [K]

CTE

[1/K

]

8 K10

010

110

210

310

410

-24

10-22

10-20

10-18

frequency [Hz]

ther

mal

noi

se [m

/ H

z]


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0 50 100 150 200 250 300-0.5

0

0.5

1

1.5

2

2.5

3x 10

-6

temperature [K]

CTE

[1/K

]

10 K10

010

110

210

310

410

-24

10-22

10-20

10-18

frequency [Hz]

ther

mal

noi

se [m

/ H

z]


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0 50 100 150 200 250 300-0.5

0

0.5

1

1.5

2

2.5

3x 10

-6

temperature [K]

CTE

[1/K

]

12 K10

010

110

210

310

410

-24

10-22

10-20

10-18

frequency [Hz]

ther

mal

noi

se [m

/ H

z]


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0 50 100 150 200 250 300-0.5

0

0.5

1

1.5

2

2.5

3x 10

-6

temperature [K]

CTE

[1/K

]

14 K10

010

110

210

310

410

-24

10-22

10-20

10-18

frequency [Hz]

ther

mal

noi

se [m

/ H

z]


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0 50 100 150 200 250 300-0.5

0

0.5

1

1.5

2

2.5

3x 10

-6

temperature [K]

CTE

[1/K

]

16 K10

010

110

210

310

410

-24

10-22

10-20

10-18

frequency [Hz]

ther

mal

noi

se [m

/ H

z]


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0 50 100 150 200 250 300-0.5

0

0.5

1

1.5

2

2.5

3x 10

-6

temperature [K]

CTE

[1/K

]

18 K10

010

110

210

310

410

-24

10-22

10-20

10-18

frequency [Hz]

ther

mal

noi

se [m

/ H

z]


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0 50 100 150 200 250 300-0.5

0

0.5

1

1.5

2

2.5

3x 10

-6

temperature [K]

CTE

[1/K

]

20 K10

010

110

210

310

410

-24

10-22

10-20

10-18

frequency [Hz]

ther

mal

noi

se [m

/ H

z]


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0 50 100 150 200 250 300-0.5

0

0.5

1

1.5

2

2.5

3x 10

-6

temperature [K]

CTE

[1/K

]

22 K10

010

110

210

310

410

-24

10-22

10-20

10-18

frequency [Hz]

ther

mal

noi

se [m

/ H

z]


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0 50 100 150 200 250 300-0.5

0

0.5

1

1.5

2

2.5

3x 10

-6

temperature [K]

CTE

[1/K

]

24 K10

010

110

210

310

410

-24

10-22

10-20

10-18

frequency [Hz]

ther

mal

noi

se [m

/ H

z]


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0 50 100 150 200 250 300-0.5

0

0.5

1

1.5

2

2.5

3x 10

-6

temperature [K]

CTE

[1/K

]

26 K10

010

110

210

310

410

-24

10-22

10-20

10-18

frequency [Hz]

ther

mal

noi

se [m

/ H

z]


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0 50 100 150 200 250 300-0.5

0

0.5

1

1.5

2

2.5

3x 10

-6

temperature [K]

CTE

[1/K

]

28 K10

010

110

210

310

410

-24

10-22

10-20

10-18

frequency [Hz]

ther

mal

noi

se [m

/ H

z]


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0 50 100 150 200 250 300-0.5

0

0.5

1

1.5

2

2.5

3x 10

-6

temperature [K]

CTE

[1/K

]

30 K10

010

110

210

310

410

-24

10-22

10-20

10-18

frequency [Hz]

ther

mal

noi

se [m

/ H

z]


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0 50 100 150 200 250 300-0.5

0

0.5

1

1.5

2

2.5

3x 10

-6

temperature [K]

CTE

[1/K

]

40 K10

010

110

210

310

410

-24

10-22

10-20

10-18

frequency [Hz]

ther

mal

noi

se [m

/ H

z]


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0 50 100 150 200 250 300-0.5

0

0.5

1

1.5

2

2.5

3x 10

-6

temperature [K]

CTE

[1/K

]

50 K10

010

110

210

310

410

-24

10-22

10-20

10-18

frequency [Hz]

ther

mal

noi

se [m

/ H

z]


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0 50 100 150 200 250 300-0.5

0

0.5

1

1.5

2

2.5

3x 10

-6

temperature [K]

CTE

[1/K

]

60 K10

010

110

210

310

410

-24

10-22

10-20

10-18

frequency [Hz]

ther

mal

noi

se [m

/ H

z]


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0 50 100 150 200 250 300-0.5

0

0.5

1

1.5

2

2.5

3x 10

-6

temperature [K]

CTE

[1/K

]

70 K10

010

110

210

310

410

-24

10-22

10-20

10-18

frequency [Hz]

ther

mal

noi

se [m

/ H

z]


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0 50 100 150 200 250 300-0.5

0

0.5

1

1.5

2

2.5

3x 10

-6

temperature [K]

CTE

[1/K

]

80 K10

010

110

210

310

410

-24

10-22

10-20

10-18

frequency [Hz]

ther

mal

noi

se [m

/ H

z]


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0 50 100 150 200 250 300-0.5

0

0.5

1

1.5

2

2.5

3x 10

-6

temperature [K]

CTE

[1/K

]

90 K10

010

110

210

310

410

-24

10-22

10-20

10-18

frequency [Hz]

ther

mal

noi

se [m

/ H

z]


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0 50 100 150 200 250 300-0.5

0

0.5

1

1.5

2

2.5

3x 10

-6

temperature [K]

CTE

[1/K

]

100 K10

010

110

210

310

410

-24

10-22

10-20

10-18

frequency [Hz]

ther

mal

noi

se [m

/ H

z]


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0 50 100 150 200 250 300-0.5

0

0.5

1

1.5

2

2.5

3x 10

-6

temperature [K]

CTE

[1/K

]

110 K10

010

110

210

310

410

-24

10-22

10-20

10-18

frequency [Hz]

ther

mal

noi

se [m

/ H

z]


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0 50 100 150 200 250 300-0.5

0

0.5

1

1.5

2

2.5

3x 10

-6

temperature [K]

CTE

[1/K

]

115 K10

010

110

210

310

410

-24

10-22

10-20

10-18

frequency [Hz]

ther

mal

noi

se [m

/ H

z]


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0 50 100 150 200 250 300-0.5

0

0.5

1

1.5

2

2.5

3x 10

-6

temperature [K]

CTE

[1/K

]

120 K10

010

110

210

310

410

-24

10-22

10-20

10-18

frequency [Hz]

ther

mal

noi

se [m

/ H

z]


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0 50 100 150 200 250 300-0.5

0

0.5

1

1.5

2

2.5

3x 10

-6

temperature [K]

CTE

[1/K

]

125 K10

010

110

210

310

410

-24

10-22

10-20

10-18

frequency [Hz]

ther

mal

noi

se [m

/ H

z]


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0 50 100 150 200 250 300-0.5

0

0.5

1

1.5

2

2.5

3x 10

-6

temperature [K]

CTE

[1/K

]

130 K10

010

110

210

310

410

-24

10-22

10-20

10-18

frequency [Hz]

ther

mal

noi

se [m

/ H

z]


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0 50 100 150 200 250 300-0.5

0

0.5

1

1.5

2

2.5

3x 10

-6

temperature [K]

CTE

[1/K

]

140 K10

010

110

210

310

410

-24

10-22

10-20

10-18

frequency [Hz]

ther

mal

noi

se [m

/ H

z]


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0 50 100 150 200 250 300-0.5

0

0.5

1

1.5

2

2.5

3x 10

-6

temperature [K]

CTE

[1/K

]

150 K10

010

110

210

310

410

-24

10-22

10-20

10-18

frequency [Hz]

ther

mal

noi

se [m

/ H

z]


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0 50 100 150 200 250 300-0.5

0

0.5

1

1.5

2

2.5

3x 10

-6

temperature [K]

CTE

[1/K

]

200 K10

010

110

210

310

410

-24

10-22

10-20

10-18

frequency [Hz]

ther

mal

noi

se [m

/ H

z]


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0 50 100 150 200 250 300-0.5

0

0.5

1

1.5

2

2.5

3x 10

-6

temperature [K]

CTE

[1/K

]

250 K10

010

110

210

310

410

-24

10-22

10-20

10-18

frequency [Hz]

ther

mal

noi

se [m

/ H

z]


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0 50 100 150 200 250 300-0.5

0

0.5

1

1.5

2

2.5

3x 10

-6

temperature [K]

CTE

[1/K

]

300 K10

010

110

210

310

410

-24

10-22

10-20

10-18

frequency [Hz]

ther

mal

noi

se [m

/ H

z]


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Thermal Noise – Adding Suspension


Thermal bath

„Universe“

TM

5 m j = 10-4

1 m, dia. 3 mmj = 2×10-9

300 K

5 K

20 K

[S. Hild]

10 km

simplified layout (4 suspended masses):

100

101

102

103

104

10-12

10-10

10-8

10-6

10-4

10-2

frequency [Hz]

mec

hani

cal l

oss

suspension loss (lowest stage):

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Thermal Noise – Adding Suspension


Thermal bath

„Universe“

TM

5 m j = 10-4

1 mj = 2×10-9

300 K

5 K

20 K

100

101

102

103

10410

-28

10-26

10-24

10-22

10-20

frequency [Hz]

ther

mal

noi

se [1

/ H

z]

mirrorpendulumviolintotalET design

sensitivity goal can be reached, additional „help“ is needed at low frequencies (artificial lowering of pendulum frequency needed – actively/passivly)

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Cooling Issues through the suspension

• cooling through fibre• target temperature: below 22 K

• thermal bath:– technically limited to 2-5 K – no huge advantage to go for 2 K from a thermal conductivity point

of view (limitation through geometry, low thermal conductivity at T < 10 K)

– however, 2 K allows use of suprafluid helium with much reduced mechanical disturbances


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• maximum cooling power is very low (L = 1m, Tbath = 2 K, 4 fibres)


Tmirror [K] Diameter [mm] Pmax [mW]20 3 480

5 13008 3400

15 3 2705 7408 1900

10 3 1005 2708 690

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• highest possible thermal conductivity needed

• investigation optical absorption in silicon (at 1550 nm unknown)

• strong reduction of introduced thermal load needed

– reduction of incident laser power(Xylophon concept, 2 detectors, low frequency detector with

low laser power e.g. 18 kW)

– very carefull dealing with scattered light needed (additional heating of test masses)


[Hild et al. 2010]

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Conclusion

• crystalline materials are candidate materials for 3rd generation detectors

• cooling necessary to reduce thermo-elastic noise

• high thermal conductivity is used to extract heat, however minimum thermal load should have very high priority (scatter!)

• thermal noise can be reduced below the requirements with reasonable materials (silicon) and R&D (loss measurments, optics absorption, coating research,…)


Thermal noise and material issues for ET

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