Detectors and Readout
3.4 TES Bolometer Basics
the bare silicon. The completed tile will be heat sunk to the focal plane unit through gold wire bonds from this gold “picture frame.”
The second step in releasing the bolometer islands is an etch with a deep trench etcher using a thick layer of patterned photoresist. This etch makes deep holes around the bolome- ter island and also cuts the wafer into a 7.3 cm square. The deep trench etcher etches deep, narrow vertical holes, so the wafer is then exposed to XeF2 gas to undercut and complete the release (thermal isolation) of the island. Extra holes in the interior of the island aid the undercutting (see Figure 3.7). Removing the photoresist and cleaning then complete the tile fabrication. Extensive electrical checks are performed at JPL to locate wiring bus and antenna shorts to the ground plane. Any device with a TES bias line short to ground is not electrically connected when the tile is mounted on the focal plane.
We use the alternate parameterization
Plegs= GT0
β+ 1
TT ES
T0
β+1
− Tsub
T0
β+1
, (3.3)
where the value of Gdepends on T0, which is a free parameter chosen to reflect the tem- perature scales of interest. This is a convenient because the derivatives take the simple forms
dPlegs
dTsub
=G Tsub
T0
β
and dPlegs
dTT ES
=G TT ES
T0
β
. (3.4)
It is often convenient to choose T0 = Tc, where Tc is the transition temperature of the superconductor. In this context the exact definition of Tc is unimportant because the transition occurs over a very narrow temperature range. With this selection, when the TES is in its transition (TT ESTc) we have
dPlegs
dTT ES =Gc, (3.5)
and
Plegs= GcTc
β+ 1
1− Tsub
Tc
β+1
. (3.6)
When specifically studying the properties of fabricated legs, it is convenient to quote a value ofG that is independent ofTc (a property of the TES, not the legs). For historical reasons we often chooseT0= 450 mK, so
Plegs= (G450)(450 mK) β+ 1
TT ES
450 mK β+1
−
Tsub
450 mK β+1
. (3.7)
The variableG450characterizes the magnitude of the thermal conductance whileβdescribes the strength of the power law. Both parameters depend on the geometry and material makeup of the structures that comprise the supporting legs.
Spider’s antenna-coupled bolometers are not designed to absorb radiation directly on the bolometer island. Instead, radiation is absorbed by a coherent slot antenna array and then that power (Q) is dissipated by a resistor on the island. This distinction does not notably effect the operation of the bolometer. The slot antenna array is described in more detail in§3.2.
(a)
Plegs
Substrate ~ 300 mK Island ~ 500 mK
PJoule
(from TES)
Gc ~ 20 pW/K Q (from antenna)
(b)
BIAS SHUNT TES
SQUID
Figure 3.11: (a) The TES thermal circuit. Antenna power and Joule power from the TES heat the bolometer island which is weakly thermally coupled to a cold substrate. (b) The TES electrical circuit. A small shunt resistor (3 mΩ) is placed in parallel with the TES (variable,∼20–30 mΩ) to establish a voltage bias. The TES branch is inductively coupled to the SQUID readout.
Spideruses Transition Edge Sensors (TES’) as thermistors. The Joule power dissipated on the bolometer island by the TES is given by
PJ oule=IT ES2 RT ES = VT ES2 RT ES
. (3.8)
Inductive coupling of the TES branch to a current sensing SQUID permits the measurement ofIT ESfrom which we can calculateRT ES andPJ oule, as explained in the following section.
Electrical Circuit
The bolometer electrical circuit is shown in Figure 3.11b. The bias voltage Vbias is the only dynamically adjustable user input. In normal operation, this bias voltage is fixed to a value chosen such that the heat dissipationPJ oule drives the TES bolometer into its transition. The resistances of the series resistor (hundreds of ohms) and parallel shunt resistor (3 mΩ) are known. The normal state resistance of the TES is about ten times that of the shunt resistor. For optimal stability and performance, bias voltages are selected such that the resistance of the TES is60% of its normal state resistance. Therefore in standard operation, most of the bias current flows through the shunt resistor branch of the circuit, establishing a fixed voltage bias across the TES.
The only property of the circuit that is dynamically measured is the current through the TES branch of the circuit. This is measured by inductive coupling to a multiplexed Superconducting Quantum Interference Device (SQUID) system, described in §3.5. The
measured current is used to calculate the resistance of the TES, given by RT ES =Rshunt
Vbias
RseriesIT ES −1
, (3.9)
as well as the voltage across the TES, given by VT ES=Rshunt
Vbias
Rseries −IT ES
. (3.10)
Let us examine the properties of a TES transition. First we apply a largeVbiassufficient to saturate the TES in its normal state. If the device is superconducting, there will be no Joule power dissipation, and it will remain in the superconducting state. We pulse the heaters on the detector tiles for 1 s to drive the devices normal. After the tile temperatures settle, we record data while incrementally decreasing the bias through the transition to the superconducting state (using theramp tes bias command while in data mode 10). In examining this data, we frequently plot the I-V curve. An example is shown in the top left of Figure 3.12. The superconducting, transition, and normal regions are clearly visible. To see whatVbiasvalues will put the TES into its transition, we plotRT ES(top right of figure).
To relate back to the power equations which govern the thermal evolution of the system, we calculate the power dissipated by the TES, PJ oule. Plotting this power against RT ES
(lower left of figure), we see that PJ oule plateaus while the TES is on transition. This is no surprise given the equilibrium thermal condition (Equation 3.1), as we are not changing the optical loadQ, and the cooling provided by the legs is nearly constant because TT ES
changes very little as the TES passes through its transition. The power level of this plateau is the saturation power (Psat). This is the amount of Joule power that must be dissipated by the TES itself to keep the TES in its transition. The addition of power (e.g., optical power) in excess ofPsat would drive the device off of the superconducting transition and in to the normal state. Measuring Psat at a variety of different substrate temperaturesTsub
with constant optical power Qenables fitting for the conductance properties of the Si3N4 legs, parameterized byG450 and β (Equation 3.7). For a dark measurement (Q= 0), the PJ oule= 0 corresponds to the TES transition temperatureTc.
0 20 40 60 80 0
20 40 60
Vbias [ mV ] I TES [ μA ]
Normal Superconducting
In transition
0 20 40 60 80
0 10 20 30 40 50
Vbias [ mV ] R TES [ mΩ ]
Super−
conducting
In transition Normal
0 20 40
0 2 4 6 8
RTES [ mΩ ]
P Joule [ pW / K ] In transition
Normal
300 400 500
0 1 2 3 4
Tsub [ mK ] P Joule in transition [ pW ]
Gc = 19.4 pW / K G450 = 14.4 pW / K
β = 1.99 Tc = 523 mK
Figure 3.12: Top left: An example of a measured I-V curve. When the TES passes through the low end of its transition, it becomes unstable and the SQUID system loses lock, in- troducing an arbitrary offset in the data. We correct for this by forcing the projection of the normal branch to intersect the origin. Top right: The calculated R-V curve, which is useful in selecting a bias voltage. Bottom left: The Joule power dissipated by the TES as a function of TES resistance. The Joule power is nearly constant while the TES is on transition assuming the optical powerQis stable. Bottom right: The TES Joule power on transition of our example device at ten different substrate temperatures withQ= 0. Curve fitting givesG, β, andTc.
Tc
0 Rn
Temperature
Resistance NTD Ge
TES Figure 3.13: Comparison of TES (su- perconductor) and NTD Ge (semicon- ductor) thermistor response functions.
Electrothermal Feedback
Earlier generations of bolometers utilized neutron transmutation doped (NTD) germanium semiconductor thermistors. Transition edge sensor (TES) bolometers replace these semi- conductor thermistors with superconductor thermistors. As shown in Figure 3.13, TES thermistors have a much steeper response function but a smaller operational range than NTD thermistors. Clearly, superconducting thermistors only exhibit significant response to temperature changes in the narrow transition between their superconducting (RT ES = 0) and normal (RT ES = Rn) states. Spider’s bolometers are maintained at a temperature within their transition by voltage biasing to take advantage of negative electrothermal feed- back. This application of feedback was proposed by Kent Irwin [63], and this section follows Irwin and Hilton’s seminal review paper [64].
The resistance of a TES is sensitive to temperature (TT ES) and current (IT ES).
αI(RT ES) = TT ES RT ES
∂RT ES
∂TT ES
IT ES
(3.11) βI(RT ES) = IT ES
RT ES
∂RT ES
∂IT ES
TT ES
(3.12)
When a small change in optical loadingδQperturbs the temperature of the TES (TT ES = Tc+δT), a change in resistance is produced (RT ES =R0+δR). Using linear approximations,
Cd(δT)
dt = PJ oule−Plegs+Q (3.13)
= (PJ oule,0−Plegs,0+Q0) +
dPJ oule
dRT ES
δR−
dPlegs dTT ES
δT+δQ
= 0 +
dPJ oule
dRT ES
αIR0
Tc δT
−GcδT +δQ
= −
−αIR0
Tc
dPJ oule
dRT ES
+Gc
δT +δQ.
For superconducting thermistorsαI is positive. The derivativedPJ oule/dRT ES is negative in a voltage-biased configuration (constantVT ES) and positive in a current-biased configu- ration (constantIT ES). We select a voltage bias configuration (Figure 3.11b, and discussed in the previous section) to achieve negative electrothermal feedback, so
Cd(δT)
dt =−(L+ 1)GcδT+δQ, (3.14)
where the loop gain
L ≡ PJ ouleαI
TcGc
. (3.15)
Both the changing Joule dissipation and the cooling power of the legs act to restore the temperature of the TES to equilibrium. Superconducting thermistors are thus easily biased into stable equilibrium in their transitions. ForSpider,L 1 so for transient response the removal of Joule power dominates over cooling through the legs. Electrothermal feedback improves linearity and makes the bolometers much faster than the natural thermal time constant (C/g). This increase in speed relative to NTD bolometers enables time multiplexed readout.