Test masses of future laser interferometric gravitational-wave detectors will be made of high-purity silicon and cooled, in particular, to 123 K in the LIGO Voyager project. Electrostatic actuators are supposed to be used to tune the test mass position. Capacitive coupling of the actuator electrodes with the silicon test mass results in the mechanical loss caused by electric currents flowing in silicon having a finite resistivity. This loss is a cause of additional thermal noise. In this study, we present the results of temperature dependence of the electric field induced loss in the bending vibration mode of commercial disk-shaped undoped silicon wafers in the temperature range of 100–295 K.

1.
R. X.
Adhikari
,
K.
Arai
,
A. F.
Brooks
et al, “
A cryogenic silicon interferometer for gravitational-wave detection
,”
Classical Quantum Gravity
37
,
165003
(
2020
).
2.
M.
Punturo
,
M.
Abernathy
,
F.
Acernese
et al, “
The Einstein Telescope: A third-generation gravitational wave observatory
,”
Classical Quantum Gravity
27
,
194002
(
2010
).
3.
E. D.
Hall
,
K.
Kuns
,
J. R.
Smith
et al, “
Gravitational-wave physics with Cosmic Explorer: Limits to low-frequency sensitivity
,”
Phys. Rev. D
103
,
122004
(
2021
).
4.
L. G.
Prokhorov
and
J.
Kissel
, “
Interaction of the ESD with electrical charges of the test masses in Advanced LIGO
,” No. LIGO-G1600699-v1,
2016
.
5.
S.
Rowan
,
S.
Twyford
,
R.
Hutchins
, and
J.
Hough
, “
Investigations into the effects of electrostatic charge on the Q-factor of a prototype fused silica suspension for use in gravitational wave detectors
,”
Classical Quantum Gravity
14
,
1537
1543
(
1997
).
6.
V. P.
Mitrofanov
,
N. A.
Styazhkina
, and
K. V.
Tokmakov
, “
Damping of the test mass oscillations caused by multistrip electrostatic actuator
,”
Phys. Lett. A
278
,
25
29
(
2000
).
7.
M. J.
Mortonson
,
C. C.
Vassiliou
,
D. J.
Ottaway
,
D. H.
Shoemaker
, and
G. M.
Harry
, “
Effects of electrical charging on the mechanical Q of a fused silica disk
,”
Rev. Sci. Instrum.
74
,
4840
4847
(
2003
).
8.
E.
Bonilla
,
P.
Giuliani
,
B.
Lantz
, and
A.
Buikema
, “
Method for electromechanical modeling of Johnson noise in Advanced LIGO
,”
Classical Quantum Gravity
38
,
025014
(
2021
).
9.
P.
Campsie
,
J.
Hough
,
S.
Rowan
, and
G.
Hammond
, “
Measurement of noise created by fluctuating electrostatic charges on dielectric surfaces using a torsion balance
,”
Classical Quantum Gravity
31
,
175007
(
2014
).
10.
See https://dcc.ligo.org/LIGO-T2100298/public for “
Instrument Science White Paper 2021, LIGO Document: LIGO-T2100298-v2.
11.
G.
Cagnoli
,
M.
Lorenzini
,
E.
Cesarini
et al, “
Mode-dependent mechanical losses in disc resonators
,”
Phys. Lett. A
382
,
2165
2173
(
2018
).
12.
G.
Vajente
,
M.
Fazio
,
L.
Yang
et al, “
Method for the experimental measurement of bulk and shear loss angles in amorphous thin films
,”
Phys. Rev. D
101
,
042004
(
2020
).
13.
K.
Numata
,
G. B.
Bianc
,
N.
Ohishi
et al, “
Measurement of the intrinsic mechanical loss of low-loss samples using a nodal support
,”
Phys. Lett. A
276
,
37
46
(
2000
).
14.
Y. Yu.
Klochkov
,
L. G.
Prokhorov
,
M. S.
Matiushechkina
et al, “
Using silicon disk resonators to measure mechanical losses caused by an electric field
,”
Rev. Sci. Instrum.
93
,
014501
(
2022
).
15.
L. G.
Prokhorov
,
V. P.
Mitrofanov
,
B.
Kamai
et al, “
Measurement of mechanical losses in the carbon nanotube black coating of silicon wafers
,”
Classical Quantum Gravity
37
,
015004
015016
(
2020
).
16.
See https://comsol.com/comsol-multiphysics for “
COMSOL Multiphysics Simulation Software
.”
17.
P. D.
Desai
, “
Thermodynamic properties of iron and silicon
,”
J. Phys. Chem. Ref. Data
15
,
967
984
(
1986
).
18.
C. Y.
Ho
,
R. W.
Powell
, and
P. E.
Liley
, “
Thermal conductivity of the elements
,”
J. Phys. Chem. Ref. Data
1
,
279
421
(
1972
).
19.
R.
Lifshitz
and
M. L.
Roukes
, “
Thermoelastic damping in micro- and nanomechanical systems
,”
Phys. Rev. B
61
,
5600
5609
(
2000
).
20.
Y.
Yang
,
T.
Ono
, and
M.
Esashi
, “
Surface effects and high quality factors in ultrathin single-crystal silicon cantilevers
,”
Appl. Phys. Lett.
77
,
3860
3862
(
2000
).
21.
E. H.
Rhoderick
, “
The physics of Schottky barriers
,”
J. Phys. D
3
,
1153
1169
(
1970
).
22.
H.
Yu
,
M.
Schaekers
,
K.
Barla
et al, “
Contact resistivities of metal-insulator-semiconductor contacts and metal-semiconductor contacts
,”
Appl. Phys. Lett.
108
,
171602
(
2016
).
23.
See https://www.pvlighthouse.com.au/resistivity for calculation of the resistivity and the carrier mobilities of a semiconductor based on the dopant concentration and temperature.
24.
S. S.
Li
and
W. R.
Thurber
, “
The dopant density and temperature dependence of electron mobility and resistivity in n-type silicon
,”
Solid-State Electron.
20
,
609
616
(
1977
).
25.
J.
Krupka
,
J.
Breeze
,
A.
Centeno
et al, “
Measurements of permittivity, dielectric loss tangent, and resistivity of float-zone silicon at microwave frequencies
,”
IEEE Trans. Microwave Theory Tech.
54
,
3995
4001
(
2006
).
26.
M.
Li
,
S.
Chen
,
Y.
Liu
et al, “
Investigation on time-dependent behavior of resistivity in high-resistivity silicon wafers
,”
Mater. Sci. Semicond. Process.
151
,
106995
(
2022
).
27.
G. J.
Gerardi
,
E. H.
Poindexter
, and
P. J.
Caplan
, “
Interface traps and Pb centers in oxidized (100) silicon wafers
,”
Appl. Phys. Lett.
49
,
348
352
(
1986
).
28.
T.
Tanikawa
,
K.
Yoo
,
I.
Matsuda
et al, “
Nonmetallic transport property of the Si(111)7 × 7 surface
,”
Phys. Rev. B
68
,
113303
(
2003
).
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