O'V' Fefelov, J' Bergli, Y' M' Galperin

1
O.V. Fefelov, J. Bergli, Y. M. Galperin AMCS
group, Department of Physics, University of Oslo
Why we need bolometers?
Historical background
The first infra-red detector called bolometer
was constructed by Samuel Pierpont Langley in
1878.
The 2006 Nobel prize in physics was granted to
George F. Smoot and John C. Mather "for their
discovery of the blackbody form and anisotropy of
the cosmic microwave background
radiation. Substantial part of the results were
obtained by bolometers attached to baloons.
(BOOMERANG program)
The first bolometer was very sensitive and could
detect 0.00001K temperature difference using a
bridge scheme. It was used for investigation of
the Sun radiation. In 1961 the first
semiconductor bolometer was constructed and its
sensitivity allowed studies of stars
radiation. In 1980s it was combined with a
superconductor thermometer to further improve the
sensitivity.
Samuel Pierpont Langley (1834-1906) was a famous
astronomer, pioneer of aviation and inventor of a
bolometer.
George F. Smoot
The sky in infra-red range. In this range a
bolometer is the most sensitive detector.
Bolometers helped to prove that our world is flat.
Langley's 1896 quarter scale aircraft model in
his workshop.
John C. Mather
Results
A bolometer consists of two parts an absorber
and a thermometer. The absorber is heated up by
incident radiation. Usually it is a very thin
membrane (several hundreds nanometers) that is
attached to a heat sink by thin wires. Modern
bolometers are cooled down to temperature
10mK. Bolometers can measure radiation flow in a
very wide frequency range from several nanometers
to several millimeters.
If we want to increase sensitivity of a bolometer
we should optimize either heat capacity of the
absorber or thermal resistance between absorber
and heat sink. It depends on response time t of a
bolometer If we measure energy pulse
shorter than t we should decrease the heat
capacity C. In the opposite case for long pulses
we should decrease the thermal resistance
R. Heat capacity of the absorber can be decreased
by 1. decreasing of temperature. (Limited by
cooling system) 2. decreasing of the thickness b
of the absorber. 3. decreasing of the absorber
area. (Characteristic size of the absorber cannot
be smaller than wavelength of light)
Thermal balance in a bolometer
1 heat sink 5 wires 6 thin membrane
is the incident flow of energy
is the energy flow from absorber to the heat sink
In case of small temperature difference
Pin
is the thermal conductance between the absorber
and the heat sink is the heat capacity of the
absorber
Pout
Superconductor thermometer is one of the most
sensitive methods for precise measurements of low
temperatures. It exploits a very steep dependence
of superconductor resistivity around transition
temperature.
A thin membrane is very flexible therefore
flexural vibrations have a very low frequency.
And they can be excited at very low temperatures
when other vibrations are frozen
This leads to a very unusual and counterintuitive
dependence of the membrane heat capacity of its
thickness
Heat capacity of a thin membrane at very low
temperatures is determined by phonons (vibrations
of crystal lattice). Dispersion laws of phonons
are different for a membrane and a bulk material.
The difference is important at low T when the
mean wavelength of phonons is greater than the
membrane thickness.
Energy
Fast increase as 1/b
Six lowest branches of vibrations in a membrane
Thick membrane
Thin membrane
3D - body
temperature
Optimal thickness for a bolometer
Wave vector k
The optimal thickness of a membrane that
corresponds to minimal heat capacity was found
for different materials and different
temperatures was calculated. It was shown that
optimal thickness increases for lower
temperatures. For modern bolometers that work at
10 mK the optimal thickness is about 2
micrometers.
For bulk material all three lowest branches of
phonons are linear for small wave vectors. In
case of membrane there is a quadratic branch
flexural or bending vibrations

• Conclusions
• An absorber with the lowest heat capacity is
  desirable for bolometers, therefore the best
  performance has always been expected for free
  standing membranes with the smallest thickness.
• We demonstrate that the heat capacity of a thin
  membrane has a minimum at a certain thickness,
  thus there exists an optimal membrane thickness.

This work was supported by the Research Council
of Norway, Project No. 142191 (NANOMAT)