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Substrate specifications for the ET
mirrors
- ongoing research and current status Ronny Nawrodt
Annual Meeting, Budapest
24/11/2010
Institut für Festkörperphysik, Friedrich-Schiller-Universität Jena
Sonderforschungsbereich Transregio 7 „Gravitationswellenastronomie“
Institute for Gravitational Research, University of Glasgow
Einstein Telescope Design Study, WP2 „Suspension“
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Overview of the Talk
• motivation
• material parameters
• optical properties of silicon
• thermal noise
• availability of bulk materials
• (ongoing) R&D
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Motivation
thermal
noise
optical
requirements
cryogenic
mirror
thermal
requirements
• optimisation process based on requirements and properties
of the materials
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Starting point
• ET HF detector is based on well known fused silica technology
at room temperature  not within the focus of this talk
• ET LF detector operates at cryogenic temperatures based on
crystalline substrate materials (sapphire, silicon)
• initial starting point:
necessary substrate mass due to radiation pressure noise
needed substrate mass ~200 kg
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Parameters needed
• thermal parameters
– well known for different materials and impurity levels
• mechanical parameters
– well known for most bulk materials at 300 K
– (good) values/upper limits for coatings/bonds
– intensive studies currently ongoing (e.g. mechanical loss)
• optical properties
– most of them known at room temperature
– some values available temperature dependent – but often not in
the temperature/wavelength range needed
• all values dependet on impurity/doping concentration
 large parameter field
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Optical Properties of Silicon
• silicon – optical material for IR applications (typ. > 2…5 µm)
– typical applications are in the MID IR region
– oxygen causes local absoption bands around 6 and 9 µm which are
avoided by high purity FZ silicon ( „optical silicon“)
• silicon:
– indirect semiconductor  absorption near or below the gap energy
needs phonons  strong temperature dependence
– re-emission of a significant amount of absorbed radiation as
luminescence radiation around 1.1 eV  not all absorbed photons
create heat  calorimetriy measurements
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Optical Absorption of Silicon
• simplified electronic band structure
k
CB
VB
indirect transition
direct transition
phonon contribution
Dk = 0
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photons do not
carry momentum
Dk = kphonon
Ephoton + Ephonon = E
 photons with E < Egap=1.1eV can be
absorbed by assistance of phonons
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Optical Absorption of Silicon
1 phonon
2 phonons
phonon
3 phonons
photon
300 K
[Keeves et al., J. Appl. Phys.]
• density of phonons is strongly temperature dependent
• much smaller absorption can be expected at low temperatures
 measurements needed
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Thermo-refractive coefficient
• important for cavity coupler, parameter =dn/dT unknown at
low temperatures
1550 nm
measurements exist for n(T)
down to 30 K (only 1
reference available!)
n(T0) = const.
(due to 3rd law of thermodynamics)
behaviour unknown
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Thermo-refractive coefficient
• most likely: continous decrease of n(T) down to 0 K
n ~ 1/Egap
based on
measurements
• suggested value for dn/dT at 20 K: < 10-6 K-1 (conservative
value!)
• extrapolation below 20 K not serious, indications predict further
decrease of dn/dT
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Mirror Thermal Noise for ET-LF
• TN estimates based on 2 ETM, 2 ITM
(no beam splitter)
Silicon
Sapphire
• calculated thermo-refractive contribution in silicon is large due to upper
limit value for dn/dT ~ 10-6 K-1  measurements needed
• bulk thermo-elastic noise starts dominating above ~22 K
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Availability of bulk materials
• Fused Silica
– large pieces available
– „simple“ technique due to amorphous state (fused silica = glass)
– remelting of small pieces to one large piece is possible
• Sapphire
– largest crystal grown: dia. 330 mm x 200 mm
– crystal growing techniques provide larger pieces
 No demand for larger pieces in industry or military applications
 High price for large samples can be expected.
• Silicon
– currently up to 16 inch diameter available for semiconductor
industry
– Crystal growing technique allows much larger samples, industry
pushed for 18 and 20 inch samples within the next 5 years
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Crystalline Silicon and Size Limitations
• Czochralski grown
• Float Zone grown
• limit: mechanical strength of
seed crystal
• high oxygen and carbon
concentration (1018 cm-3)
• limit: inductive remelting of
silicon, cost intensive technique
(not needed for standard
semiconductor applications)
• low impurity concentration
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Influence of impurities on the mechanical loss
• oxygen causes dissipation peaks in the mechanical spectrum
10
10
Czochralski - 1018 cm-3 O2
Float Zone - 1015 cm-3 O2
9
Si-O-Si induced
Mechanical loss
Q-factor
10
10
10
8
7
1
3
30
10
temperature [K]
100
300
• R&D aim: set an upper limit on impurity concentrations that are
tolerable based on the thermal noise estimates for CZ silicon
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LF interferometer – substrate material options
Sapphire
Silicon
mechanical loss
++
++
mechanical strength
+(+)*
++
optical material
+
o
thermal conductivity
++
++
polishing
-
+
size availability
-…+
+
* bond strength not sufficient (silicate bonding)
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What R&D is needed in the near future? (1)
• coating research
–
–
–
–
mechanical parameters (annealing – loss – scatter)
thermal parameters (thermal conductivity, thermal expansion)
optical parameters (absorption, scattering)
coating technology
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What R&D is needed in the near future? (2)
• bulk research
–
–
–
–
bonding techniques and ist implications on thermal noise
mechanical loss vs. impurities
thermal properties vs. impurities (suspension elements)
optical properties (n(T), dn/dT, scattering, absorption)
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Current work on optical properties
• measurement of dn/dT
– e.g. record transmission of Si sample
during cooling
expected transmission based on current
values for n(T)
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Summary and Conclusions
• ET HF detector based on currently available techniques
• ET LF requirements can be reached with current upper limits of
unknown parameters
dia. 450-500 mm
T~
10 K
1) thickness: 300 mm (for TN purposes) +
additional mass
2) thickness: 460 mm (Tref optimisation with
beam splitter needed)
• availability of the materials under investigation
• strong R&D needed on the material side to get „real“ values
and confirm the assumptions and refine upper limit estimates
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Daub, Würfel, PRL 74 (1995)
measured absorption of silicon from luminescence spectra
comparison with transmission measurements
295 K
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90 K