Thermal properties in mesoscopics: physics and ... - ResearchGate

and Rutledge, 1984). For air-bridged devices at temperatures
higher than 4 K, NEPTFN ∝ T 3/2 . Recently,
an air-bridge bolometer operating at 4.2 K was demonstrated,
showing potential for background-limited performance
when observing 300 K blackbodies (Luukanen
et al., 2005; Luukanen and Pekola, 2003). The potential
applications for these devices include passive detection
of concealed weapons under clothing, remote trace detection,
and terrestrial submillimetre-wave imaging.
C. Calorimeters: Pulsed excitation
In the limit opposite to the bolometric detection, i.e.
when the mean time between the quanta of energy arriving
at the detector exceeds the device relaxation time,
thermal detectors are known as calorimeters. While the
topic of calorimetry also encompasses heat capacity measurements
especially in mesoscopic samples, the following
discussion concentrates on the detection of radiation
only in order to keep the scope of our review in reasonable
limits. For those interested in microcalorimetry in
the sense of heat capacity measurements, we direct the
reader to references (Bourgeois et al., 2005; Denlinger
et al., 1994; Fominaya et al., 1997; Lindell et al., 2000)
and (Marnieros et al., 1999).
Cryogenic calorimeters are used today in a large variety
of applications, from the detection of weakly interacting
massive particles (WIMPs) in dark matter search (Akerib
et al., 2003; Bravin et al., 1999), X-ray (de Korte
et al., 2004; Kelley et al., 1999; Moseley et al., 1984) and
γ-ray (van den Berg et al., 2000) astrophysics to secure
optical communications (Miller et al., 2003; Nam et al.,
2004). As is the case with bolometers, calorimeters are
usually operated at temperatures below 1 K. The theory
and operation of calorimetric thermal detectors is
very similar to bolometers, and generally the theoretical
treatment above is valid. However, the optimization of
calorimetric detectors can be quite different. The quantum
of energy E deposited by either a photon, charged
particle, WIMP etc. can be determined from the temperature
rise ∆T = E/C, where C is the heat capacity
of the calorimeter. This temperature rise then decays
exponentially with a time constant τeff to its equilibrium
value. Thermometry in the calorimeters is most often
done either using semiconducting or TES thermometers,
as is the case with bolometers. In addition, thermometry
based on the change of magnetization of a paramagnetic
sensor is appealing due to its non-dissipative nature, and
has yielded some promising results (Fleischmann et al.,
2003; Schönefeld et al., 2000).
The figure of merit for a calorimeter is the energy resolution,
∆E, of full-width at half-maximum (FWHM),
related to NEP through (Moseley et al., 1984)
∆E =2 √ 2 ln 2
∞
0
4
NEP 2 (f)tot
df
−1/2
≈ 2 √ √
2 ln 2NEP(0)tot τeff, (75)
30
For a ’classic’ calorimeter with a white noise spectrum the
energy resolution is in terms of the operating temperature
and the heat capacity given by
∆E = 2 √ 2 ln 2 kBT 2 C, (76)
indicating that ∆E scales ∝ T 5/2 or ∝ T 3/2 depending
whether the heat capacity of the sensor is dominated by
the lattice or the electronic system, respectively.
In most of the devices under development today the
lattice temperature is being measured, as sufficient cross
section to the incoming energy often requires a rather
large volume of a device. An exception to the norm are
TES calorimeters optimized for optical single photon detection
for applications in secure quantum key distribution
(Nam et al., 2004), shown in Fig. 20. In these
devices, the thermal isolation is via electron-phonon decoupling.
A trade-off is made between energy resolution
and the speed of the detectors. Energy resolution of the
detectors is sufficient to determine the photon-number
state of the incoming photons, while maintaining a speed
that is adequate for fast information transfer.
FIG. 20 (Color in online edition): The energy spectrum of
a pulsed 1550 nm laser, measured with an optical TES microcalorimeter.
The peaks in the plot correspond to the
photon-number state of the incoming pulses. The inset shows
a micrograph of the devices. Figure courtesy of A.J. Miller,
NIST.
As with bolometers, the TESs currently outperform
the competition in terms of the sensitivity. The best
reported energy resolution for any energy dispersive detector
was recently obtained with a Mo-Cu calorimeter
(see Fig. 21), yielding an energy resolution of 2.38± 0.11
eV at a photon energy of 5.89 keV (Irwin and Hilton,
2005). The driving application in the development of Xray
microcalorimeters are two major X-ray astrophysics
missions planned by the European Space Agency (ESA)
and the U.S. National Astronautics and Space Administration
(NASA). Both missions, X-ray Evolving Universe
Spectroscopy (XEUS) (The European Space Agency,
2005) mission and the Constellation-X mission (NASA,
2005) will employ X-ray microcalorimeters as their primary
instrument. The energy resolution of the state of