Phonon detection

As mentioned earlier, one of the flat faces of a ZIP is photolithographically patterned with four quadrant-shaped phonon sensors, labeled A, B, C, and D in clockwise order, starting with the upper left quadrant. Figure 3.8 shows a schematic of the patterning of phonon sensors on a detector face. Each sensor consists of 1036 superconducting tungsten thin-film sensors called Transition-Edge Sensors (TES), wired in parallel, but divided into 37 tiles of 28 TESs each. Each TES is fed by superconducting aluminum fins that collect phonon energy and concentrate it in the much smaller TESs. The aluminum absorbers and TESs are together called “QETs”: Quasiparticle-trap-assisted Electrothermal-feedback Transition Edge Sensors. These are subsequently read out by SQUID-array amplifiers as explained in the next section.

3.3.2.1 Absorber fins

Phonons are collected in absorber fins made of aluminum, 350µm long, 50µm wide, and 300 nm thick. Since the crystal temperature is well below superconducting transition of 1.2 K for aluminum, the energy gap to break cooper pairs into quasiparticles is high, 2∆Al= 360µeV. Athermal phonons

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Figure 3.8: QET layout on a ZIP. Upper left: Phonon side of ZIP showing four quadrant-shaped phonon sensors and, their labels A, B, C and, D. Each phonon sensor is fabricated by tiling 37 5 mm_×5 mm templates (upper right), each with 28 QETs in grey and surrounding aluminum grid in green. Bottom: Zoom in of a single QET with aluminum absorbers in grey color and tungsten TES in blue. Figure taken from: [89].

are typically sufficiently energetic to do this and deposit their energy in the quasiparticle system, whereas thermal phonons (energy_∼kT = 3.4µeV) are unable to do so. The quasiparticles generated by the phonons diffuse through the aluminum until they recombine or find their way into the tungsten TESs. There is a region of overlap between the Al and W, where the superconducting gap transitions from that of Al to that of W. Tungsten has a lower critical temperature and hence a lower energy gap for cooper-pair breaking, 2∆W ≈24µeV. Quasiparticles entering the W TESs quickly lose energy

and fall below the high energy gap of Al, becoming unable to diffuse back into the Al. Thus the interface of the Al absorber and the W TES serves as a quasiparticle trap, concentrating energy from a large collection area into the TES. Despite micron-scale features, 28 QETs alone are therefore able to collect phonon energy from a 5 mm×5 mm area of the detector flat surface. A schematic of the phonon absorption and quasiparticle trapping in the QETs is shown in Figure 3.9.

Al Collector

W Transition-

Edge Sensor

Ge or Si

quasiparticle

diffusion

phonons

Figure 3.9: Schematic of QET. Phonons entering the aluminum absorber break cooper pairs, gen- erating quasiparticles. The quasiparticles diffuse through the aluminum and are trapped in the tungsten TESs.

3.3.2.2 Transition-Edge Sensors

Superconducting Transition-Edge Sensors (TESs) are very sensitive, high-bandwidth variable resis- tors that change resistance with temperature, and can have extremely small feature size — 1µm wide, 250µm long and 35 nm thick in CDMS II ZIPs. They are operated at their critical tempera- tureTc, partway through their superconducting transition. This transition is typically very sharp,

causing a large change in resistance for a small change in temperature, as long as the TES equilib- rium temperature is within the narrow window of the transition. This makes the TES a precision measurement tool for small inputs of energy. A detailed review of TESs is provided in [97].

TESs need to be held very close to Tc and need to repeatably return to the initial bias point

after temperature excursions caused by energy deposition. In CDMS, this is accomplished by voltage biasing the TESs. The power flowing into a TES’s electron system at temperatureTeis a combination

of Joule heating by current flowing through it (PJ=Vbias2 /RT ES), and any external power loading,

i.e., quasiparticle energy introduced in it the absorbers,Pext. The power flowing out is through the

of these is tightly coupled to the experiment’s heat bath at temperature T0 via heat sinking of the

detectors to the dilution fridge. Thus the following relation holds:

V2 bias RT ES

+Pext'Gep(Te−T0) (3.3)

The key for proper functionality of the TES is to have a suitably low Gep and a carefully selected Vbias such that the TES electron system self-heats to an equilibrium temperature equal to the

superconducting transition point. Then, upward fluctuations inPext would increase Te and hence RT ES, but would cause a drop in Joule heating and eventually restore the TES back to its equilibrium

temperature. This is called negative electrothermal feedback, and enables the TESs to be operated stably. This scheme works not only for single TESs, but for the parallel TES arrays of a ZIP phonon sensor. Even if there are slight variations inTc of individual TESs, a single voltage bias allows all

TESs to self-heat to appropriate equilibrium temperatures within the transition. This does, however, soften the sharpness of the transition and hence the resolution of the measurement.

Note that CDMS TES films are deposited with a target Tc ∼120 mK but end up with 10–20%

variations. The TESs are implanted with Fe ions after initial fabrication to uniformly tune theTc

closer to 80 mK [98].