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==History==
The first demonstrations of the superconducting transition's measurement potential appeared in the 1940's1940s, thirty years after [[Heike Kamerlingh Onnes|Onnes]]'s discovery of [[superconductivity|superconductivity]]. D.H. Andrews demonstrated firstthe afirst transition-edge [[bolometer|bolometer]], a current-biased [[tantalum]] wire which he used to measure an infrared signal,. andSubsequently thereafterhe demonstrated a transition -edge [[calorimeterCalorimeter (particle physics)|calorimeter]], made of [[niobium nitride]] andwhich was used to measure [[alpha- particles]]. <ref> D.H. Andrews ''et. al.m'', "Attenuated Superconductors i. For Measuring Infra-Red Radiation." ''Rev. Sci. Instrum.'', '''13''', 281 (1942).</ref> However, the TES detector did not gain popularity for about 50 years, due primarily to the difficulty of signal readout from such a low-[[Electrical impedance|impedance]] system. A second obstacle to the adoption of TES detectors was in optimizingachieving stable operation in the narrow superconducting transition edgeregion. [[Joule heating|Joule heating]] in a current-biased TES can lead to thermal runaway that drives the detector into the normal (non-conductingsuperconducting) state, a phenomenon known as [[electrothermal feedback]]. A solution to the readout problem has been found in superconducting quantum interference devices ([[SQUID|SQUIDs]]) which are now designed to pair effectively with the TES detectors;. theThe additional development of voltage-biased operation for TESs has facilitated wide-spread adoption of TES detectors since the late 1990's1990s.<ref name="IrwinHilton">K. D. Irwin and G. C. Hilton, "Transition-Edge Sensors," ''Cryogenic Particle Detection'', ed. C. Enss, Springer, 2005, {{doi|10.1007/10933596_3}}</ref>
==Setup, Operation, and Readout== ▼A TES single-photon detector is voltage-biased by driving a current source I<sub>bias</sub> through a load resistor R<sub>L</sub>. The voltage is chosen to put the TES in its so-called "self-biased region" where the power dissipated in the device is constant with the applied voltage. When a [[photon|photon]] is absorbed by the TES, this extra power is removed by negative [[Electrothermal_feedback|electrothermal feedback]]: the TES [[electrical_resistance|resistance]] increases, causing a drop in TES current, the dissipated Joule power in turn drops, cooling the whole device back to its equilibrium power dissipation in the self-bias region. In a common SQUID readout system, the TES is operated in series with the input coil L which is inductively coupled to a SQUID series-array. Thus a change in TES current manifests as a change in the input [[flux|flux]] to the SQUID, whose output is further amplified and read by room-temperature electronics. ▼
▲==Setup, Operationoperation, and Readoutreadout==
[[File:TES schematic.pdf|thumb|alt=Schematic of TES-SQUID circuit|Schematic of TES-SQUID circuit]]
▲AThe TES single-photon detector is voltage-biased by driving a current source I<sub>bias</sub> through a load resistor R<sub>L</sub> (see figure). The voltage is chosen to put the TES in its so-called "self-biased region" where the power dissipated in the device is constant with the applied voltage. When a [[ photon|photon]] is absorbed by the TES, this extra power is removed by negative [[ Electrothermal_feedback|electrothermal feedback]]: the TES [[ electrical_resistanceElectrical resistance|resistance]] increases, causing a drop in TES current ,; the dissipated [[Joule power ]] in turn drops, cooling the whole device back to its equilibrium power dissipationstate in the self- biasbiased region. In a common [[SQUID ]] readout system, the TES is operated in series with the input coil L which is inductively coupled to a SQUID series-array. Thus a change in TES current manifests as a change in the input [[ flux|flux]] to the SQUID, whose output is further amplified and read by room-temperature electronics.
==Functionality==
Any [[bolometer|bolometric]] sensor employs three basic components: an [[Absorption_(electromagnetic_radiation)|absorber]] of incident energy, a [[thermometer|thermometer]] for measuring this energy, and a (weak) [[Thermal_conductivity|thermal link]] to base temperature to dissipate the absorbed energy and re-cool the detector.<ref name="NIST">A. Lita ''et. al.'', ''Optics Express'' 3032 Vol.16., No.5, 2008.</ref>
===Absorber===
The simplest absorption scheme can be applied to TESs operating in the near-IR, optical, and UV regimes. These devices generally utilize a [[tungsten|tungsten]] TES as its own absorber, therebywhich absorbingabsorbs up to 20% of the inputincident radiation. <ref name = NIST2>A.J. Miller ''et. al.'', "Demonstration of a low-noise near-infrared photon counter with multiphoton discrimination," ''Appl. Phys. Lett.'', '''83''', 791-793. (2003).[http://people.bu.edu/alexserg/APL_2003.pdf ] {{doi|10.1063/1.1596723}}</ref> If high-efficiency detection is desired, the TES may be fabricated in a multi-layer [[Optical_cavity|optical cavity]] tuned to the desired operating wavelength and employing a backside mirror and frontside anti-reflection coating. Such trickstechniques can decrease the transmission and reflection from the detectors to negligibly low values, resulting in a device with a device whose efficiency in principle exceeds 99%. (In fact,; 95% detection efficiency has been observed.<ref name=NIST />) At higher energies, the primary obstacle to absorption is transmission, not reflection, and thus an absorber with high photon stopping-power and low heat capacity is desirable--; a [[Bismuth|Bismuthbismuth]] film is often employed.<ref name=IrwinHilton /> Any absorber should have low [[heat_capacity|heat capacity]] with respect to the TES. Higher heat capacity in the absorber will contribute to noise and decrease the sensitivity of the detector (since a given absorbed energy will not produce as large of a change in TES resistance). For far-IR radiation into the millimeter range, the absorption schemes arecommonly variedemploy and[[Antenna complicated,(radio)|antennas]] including resonant cavities as described above,or [[feedhorn|feedhorns]], and mores.<ref name=IrwinHilton />
=== Thermometer ===
The TES operates as a thermometer in the following manner: absorbed incident energy automatically increases the resistance of the voltage-biased sensor within its transition edgeregion, and the integral of the resulting drop in current is proportional to the energy absorbed by the detector .<ref name=NIST2 />. The output signal is proportional to the temperature change of the absorber, and thus for maximal sensitivity, a TES should have low heat capacity and a narrow transition edge. Important TES properties, including not only heat capacity but also thermal conductance and thermal noise, are strongly temperature dependent, so the choice of [[Superconductivity#Superconducting_phase_transition|transition temperature]] T<sub>c</sub> is critical to the device design. Furthermore, T<sub>c</sub> should be chosen to accommodate the available [[cryostat|cryogenic system]]. Tungsten has been a popular choice for elemental TESs as thin-film tungsten displays two phases, one with T<sub>c</sub> ~15 mK and the other with T<sub>c</sub> ~1-4 K, which can be combined to finely tune the overall device T<sub>c</sub>. <ref>A. Lita ''et. al.'', "Tuning of Tungsten Thin Film Superconducting Transition Temperature for Fabrication of Photon Number Resolving Detectors.," (2004). ''IEEE Transactions on Applied Superconductivity'', Vol. 15, No. 2, June (2005).</ref> Bilayer and multilayer TESs are another popular fabrication approach, where [[thin_film|thin filmsfilm]]s of different materials are combined to achieve the desired T<sub>c</sub>. <ref name=IrwinHilton />
===Thermal conductance===
Finally, it is necessary to tune the [[Thermal_conductivity|thermal coupling]] between the TES and the bath; a low thermal conductance is necessary to ensure that incident energy is seen by the TES rather than being lost directly to the bath,. howeverHowever, the thermal link must not be too weak, as it is necessary to cool the TES back to bath temperature after the energy has been absorbed. The two primaryTwo approaches to control the thermal link are by electron-phonon decoupling,coupling and by mechanical machining. InAt acryogenic superconductortemperatures, heat is carried not by conductionthe [[electrons|electronselectron]] but byand [[phonons|phononsphonon]], andsystems in somea casesmaterial thecan electronbecome andonly phononweakly systemscoupled. ofThe theelectron-phonon samethermal materialconductance mayis differ instrongly temperature. Tungsten is an example of such a system-dependent, and tungsten TESs exploithence the inherentthermal weakconductance phonon-electroncan couplingbe astuned theirby thermaladjusting link to bathT<sub>c</sub>. <ref name=IrwinHilton /> <ref name=NIST /> Other devices use mechanical means of controlling the thermal conductance such as building the TES on a sub-micron membrane over a hole in the substrate or in the middle of a sparse "spiderweb" structure. <ref>J. Bock ''et. al.'', "A novel bolometer for infrared and millimeter-wave astrophysics.," ''Space Science Reviews'', 74(1-2), 229-235 (1995).</ref>
==Advantages and Disadvantagesdisadvantages==
TES detectors are attractive to the scientific community for a variety of reasons. Among their most striking attributes are an unprecedented high detection efficiency customizable to wavelengths from the millimeter regime to gamma rays <ref name=IrwinHilton /> <ref name=NIST />, and a theoretical negligible background dark count level (less than 1 event in 1000 s from intrinsic [[Phonon_noisePhonon noise|thermal fluctuations]] of the device <ref name=NIST2 />). (In practice, although only a real energy signal will create a current pulse, a nonzero background level may be registered by the counting algorithm or the presence of background light in the experimental setup. Even thermal [[blackbody radiation]] may be seen by a TES optimized for use in the visible regime.)
TES single-photon detectors suffer nonetheless from a few disadvantages as compared to their [[Single-photon_avalanche_diode|avalanche photodiode]] (APD) counterparts. APDs are manufactured in small modules which count photons out-of-the-box with a [[dead_time|dead time]] of a few nanoseconds and output a TTL pulse corresponding to each photon with a jitter of tens of picoseconds. In contrast, TES detectors must be operated in a cryogenic environment, output a signal which must be further analyzed to identify photons, and have a jitter of approximately 100 ns .<ref name=NIST />. Furthermore, a single photon spike on a TES detector lasts on the order of microseconds.
==Applications==
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