INFLATION
2.3 Detector design
load is much less than 0.1 pW, even if an unreasonably high in-band emissivity is assumed. There is some reduced optical efficiency due to the added reflective surfaces and in-band absorption, but this has been measured to be less than2%at 150 GHz.
The final filter in the optical chain is a metal mesh band-defining filter with a tuned frequency cutoffof 8.3 icm. The use of this filter was motivated by an observed percent-level high-frequency spectral leak in the detectors. This measured “blue leak” was partially mitigated by changes to the detector design before theBicep2 science-grade detectors were fabricated. With the combination of these detector design changes and the presence of the metal mesh filter, this out-of-band coupling has been largely mitigated.
2.2.4 Anti-reflection coating
All of the optical elements (except for the vacuum window) were anti-reflection coated using porous Teflon, manufactured under the product name Mupor3. The porous Teflon can be tuned in both thickness and density to match the /4 criterion for impedance matching.
The anti-reflection coating was heat-bonded using a vacuum bagging procedure. Each optical element was placed in an inverted mold and coated with a thin low-density polyethylene (LDPE) layer and the porous teflon anti-reflection coating. The mold, together with the optical element and the anti-reflection coating, was enclosed in a silicone bag, which was then placed under vacuum and inserted into a convection oven (Figure 2.4). The vacuum bag ensured isobaric pressure was applied evenly to the surface during the heat bonding.
During the first few attempts at anti-reflection coating in this way, it was discovered that internal stresses significantly deformed the optical elements under thermal cycling, particularly for the HDPE lenses. As a result, a great deal of effort was made to anneal the optical elements during the manufacturing process. After following a two-stage annealing schedule, we found the lens shape to be highly repeatable and unchanged by the anti-reflection coating procedure.
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Figure 2.4: Anti-reflection coating of the Bicep2 lenses. The lens is placed in an inverted mold, coated with LDPE and the anti-reflection film, and placed in a vacuum bag. The entire assembly is then pulled under vacuum and placed in a convection oven for heat bonding.
process used to fabricate the devices.
2.3.1 Transition-Edge Sensors bolometers
The principle of operation for any bolometer is simple: An absorptive element is coupled to a ther- mally isolated temperature-sensitive resistor. Incident radiation heats the absorber, which in turn heats the resistor, which is then measured as a change in current. The TES bolometer is no differ- ent. The temperature-sensitive resistor is a superconducting film, biased onto its superconducting transition. Small changes in temperature induce corresponding changes in resistance. The previous generation of bolometers used in Bicep1 (called NTD bolometers) used semiconducting films to achieve the same function.
The bolometer must be minimally thermally coupled to the rest of the system, but must also be able to dissipate power back to the bath. For this reason, the bolometer is formed into an “island”, which is thermally coupled to the bath temperature,Tbaththrough a weak heat link of conductivity G(Figure 2.6). The device thus also naturally has some thermal time constant, determined by the conductivityGand the heat capacity of the island,C.
The TES bolometer offers several key advantages over its semi-conducting predecessor. First, when optimally biased, the resistance of the TES is a steep function of temperature, the result of which is very high responsivity. The second advantage is that TES devices can be read out using SQUID amplifiers rather than JFETs, which is a critical consideration when one considers multiplexing a large number of these devices on a single focal plane. A third advantage is that the
thermal time constant of the TES devices is much faster than for NTDs due to the much smaller heat capacity of the superconducting device. NTD-based detectors often require complicated modeling to fully characterize the temporal transfer function of the device. There is no such complication with TESs: The devices are sufficiently fast that the temporal transfer function can often be entirely ignored in analysis4. Finally, arrays of TESs can be fully lithographed onto silicon wafers, avoiding the hand assembly required for feedhorn-coupled NTDs.
The TES can be stably biased onto its superconducting transition using negative electro-thermal feedback. We consider a device with a thin film of superconducting metal with a transition tem- perature Tc, typically of order ⇠ 500 mK. A voltage bias is applied to keep the film between the superconducting and normal states. An increase in resistance results in a corresponding increase in Joule power, which in turn, drives up the temperature. As the temperature increases, the bias current decreases, along with the Joule heating, resulting in a negative feedback loop. Expressed more formally, electro-thermal feedback is the result of two coupled differential equations. Ignoring noise, we can write the thermal differential equation:
CdT
dt = PG+PJ+P. (2.3)
Here C is the heat capacity,PG is the power lost to the bath, PJ is the Joule power, andP is the incident optical power. Correspondingly, the characteristic electrical differential equation is:
LdI
dt =Vbias IRsh IR(T, I), (2.4)
whereLis the electrical inductance,Vbiasis the bias voltage,Iis the current,Rsh is the shunt resis- tance (which may also contain some parasitic resistance), andR(I, T)is the temperature-dependent resistance.
The coupling between these two differential equations comes about from the Joule power term, which is:
PJ=Vbias2 /R(T, I). (2.5)
It is useful to examine the steady-state behavior of these expressions. Setting the time derivative terms to zero, and solving for the optical powerP:
P =PG Vbias2 I
Vbias IRsh (2.6)
We conclude from this expression that in the steady-state case, if we know the various parameters of
4The speed of the TES can also be a nuisance. TES bolometers can become unstable when the thermal timeconstant and electrical timeconstant overlap. There is no such concern with NTDs.
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Normal resistance
Transition temperature
Bias point
Rdyn(⌦)
T(K)
Tc
Rnorm
(a)
Ω Ω