Report on WP1/M1: Investigation plan related to the effects of doping in silicon
P. Murray1, E. Chalkley1, S. Rowan1, J. Hough1
1
Institute of Gravitational Research, University of Glasgow, Glasgow, UK
Coordinators: V. Loriette (CNRS), M. Punturo (INFN)
Introduction
Whilst designs of the type proposed for Advanced LIGO and Advanced VIRGO should allow
major sensitivity improvements over first generation detectors, they do not reach the limits set
by the existing facilities.
In extending performance further, as is the intention for the proposed EGO gravitational wave
detector, thermal noise in the test mass substrates resulting from thermodynamic fluctuations
in temperature must be reduced. This ‘thermoelastic’ thermal noise results in displacement
noise in an interferometer through the finite coefficient of thermal expansion of the test mass
material and sets a limit to the performance of materials. This is analogous to, and in addition
to any coating thermoelastic noise. Our calculations suggest the unique combination of
thermo-mechanical properties displayed by silicon give it significant advantages over other
materials considered.
Mechanical dissipation in bulk silicon is believed in general to decrease with temperature,
thus thermal noise should also decrease.
Thermoelastic damping at room temperature, is such that the power spectral density of
thermoelastic displacement noise, x2() , [Braginsky et al 1999] is given by
 2T 2 1 ,
x 2 ( ) 
C2 2
where  is the coefficient of thermal expansion, C the heat capacity and  the thermal
conductivity of the substrate material. At very low temperatures a different scaling regime
exists [Rowan 2000, Cerdonio et al 2001] and
x 2 ( ) 
 2T 2 .

The temperature dependence of , C and  [Touloukian et al 1970], suggests thermoelastic
noise should also decrease with temperature.
However results in the literature suggest that the temperature dependence of thermal
conductivity of silicon can depend on the doping of the material. In addition at ~ 18 K and
120 K where the thermal expansion coefficient of silicon goes to zero the thermoelastic noise
should also go to zero, leaving as the principal noise source the intrinsic thermal noise in
silicon [Rowan et al 2003]. Interestingly, two "peaks" in the intrinsic dissipation at ~13 K and
~115 K have been reported - close to the nulls in thermoelastic damping [McGuigan et al
1978]. The origin of the dissipation is not well understood, but has been postulated to be
related to the doping of the material
We have thus carried out studies of the material properties and dissipative behaviour of
silicon, initially at room temperature and are commissioning cryostats in which to study
silicon properties as a function of temperature.
This studies of the properties of silicon as a function of doping are clearly of interest.
Experimental studies
We are thus using (a) bulk cylinders of silicon as samples on which to study the intrinsic
dissipation of silicon, at resonant frequencies in the kHz region where thermoelastic damping
is negligible and (b) thin silicon cantilevers, with resonant frequencies in the tens of Hz to
~1 kHz to study levels of thermo-elastic damping, in the frequency range of interest for
gravitational wave detection. The results for the studies of the cantilever samples are
described under a separate workpackage.
The bulk samples have been fabricated from both commercial boron-doped silicon and also
nominally undoped material in an attempt to identify any differences in behaviour associated
with the different doping levels.
However so far we believe that any differences we see in the samples are a result of the cut of
the sample influencing the measured Q, possibly through the effect of the crystal orientation
on mode shape and thus coupling to the support structure.
To further investigate this possibility we have procured samples of the same doping but of
different aspect ratios and cuts.
Measured loss factors for two of these samples are shown in figure 1, where the results shown
are consistent with our postulate that we are not yet measuring dopant-related dissipation, but
dissipation perhaps due to the support structure used.
14
12
[111] Silicon
[100] Silicon
Q (x10 7)
10
8
6
4
2
.
0
20000
30000
40000
50000
60000
70000
80000
Freq (Hz)
Figure 1 Measured loss factors for a number of modes of two samples of silicon of nominally
identical material, surface polish and dimensions (3” by 1”), but cut along different crystalline
axes
Previous work by Numata et al showed that for some subset of modes of a sample a support,
which contacts the sample at positions of minimum or zero displacement, can give low
support losses. We have thus constructed a prototype ‘nodal support’ system to attempt to
reduce suspension losses for these modes, and allow dopant related properties to be studied.
Colleagues in Jena are also studying the loss factors of bulk silicon samples and plans to
exchange samples for joint study are currently under discussion.
Once support losses have been reduced further we will first revisit the study of the mechanical
dissipation of doped versus undoped silicon samples.
We will then use the results of that study to inform further experiments to study silicon
samples with different levels of doping.
(a)
(b)
Figure 2 (a) Prototype nodal support system (b) Typical mode shapes for which this type of
system may be appropriate
References
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gravitational wave antennae, V.B. Braginsky, M.L. Gorodetsky and S.P. Vyatchanin, Phys.
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[Cerdonio et al 2001] Thermoelastic effects at low temperatures and quantum limits in
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D 63, e082003/1-9, 2001
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Aspen, Colorado, January 2000
[McGuigan et al 1978] Measurement of mechanical Q of single-crystal silicon at low
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W. Gutche, Journal of Low Temperature Physics, 30, 621, 1978
[Touloukian et al 1970]