4.2 Science-grade Arrays
4.2.5 Hot/Cold
for each resonator individually.
Table 4.5: Hot/Cold results. The quoted values are the (median)±(median absolute deviation), calculated using the detectors of the specified band on the specified device half-band.
Band Device Nres ∆νmm,ant[GHz] Texc[K] Pexc[pW] Pexc,ant[pW] C[GHz/nm] Cant[GHz/nm] ηant
Dark
A2L 5 – 68±36 0.2±0.1 – 0.006±0.002 – –
A2U 4 – 70±38 0.2±0.1 – 0.004±0.001 – –
B2L 6 – 149±22 0.3±0.1 – 0.003±0.000 – –
B2U 3 – 91±58 0.2±0.1 – 0.004±0.000 – –
0
A2L 4 20 36±23 0.8±0.4 0.6±0.4 0.038±0.008 0.033±0.008 0.072±0.017
A2U 10 20 28±16 0.7±0.3 0.5±0.3 0.046±0.006 0.041±0.006 0.091±0.014
B2L 6 17 34±16 0.9±0.5 0.6±0.5 0.035±0.008 0.032±0.008 0.080±0.020
B2U 6 19 24±10 0.7±0.2 0.5±0.2 0.042±0.006 0.038±0.006 0.089±0.014
1
A2L 18 27 23±15 1.1±0.7 0.9±0.7 0.078±0.005 0.073±0.005 0.118±0.009
A2U 3 25 21±3 1.1±0.3 0.9±0.3 0.079±0.004 0.075±0.004 0.133±0.007
B2L 11 22 14±11 0.6±0.4 0.3±0.4 0.066±0.004 0.063±0.004 0.128±0.009
B2U 10 23 19±4 1.0±0.2 0.7±0.2 0.078±0.009 0.073±0.009 0.138±0.018
2
A2L 20 18 25±6 0.7±0.3 0.6±0.3 0.045±0.004 0.040±0.004 0.097±0.011
A2U 11 16 35±23 0.9±0.7 0.7±0.7 0.043±0.008 0.039±0.008 0.109±0.023
B2L 20 16 16±9 0.4±0.2 0.1±0.2 0.042±0.004 0.039±0.004 0.109±0.010
B2U 12 15 26±7 0.8±0.5 0.6±0.5 0.048±0.008 0.043±0.008 0.125±0.023
3
A2L 8 16 50±9 0.8±0.1 0.7±0.1 0.028±0.006 0.022±0.006 0.063±0.016
A2U 12 11 38±14 0.7±0.3 0.5±0.3 0.032±0.010 0.027±0.010 0.103±0.036 B2L 12 13 46±17 0.7±0.4 0.5±0.4 0.025±0.003 0.022±0.003 0.073±0.011
B2U 3 10 33±3 0.3±0.1 0.1±0.1 0.018±0.005 0.014±0.005 0.059±0.021
Table 4.6: Hot/Cold results. The quoted values are the (median)±(median absolute deviation), calculated using all detectors of the specified band.
Band Nres ∆νmm,ant[GHz] Texc[K] Pexc[pW] Pexc,ant[pW] C[GHz/nm] Cant[GHz/nm] ηant
Dark 18 – 84±64 0.2±0.1 – 0.004±0.001 – –
0 26 20 29±13 0.7±0.3 0.5±0.3 0.042±0.008 0.038±0.008 0.083±0.013 1 42 24 20±10 1.0±0.5 0.7±0.5 0.076±0.009 0.071±0.008 0.125±0.015 2 63 16 24±10 0.6±0.3 0.4±0.3 0.044±0.004 0.040±0.004 0.108±0.014 3 35 13 47±14 0.8±0.3 0.6±0.2 0.026±0.007 0.022±0.007 0.074±0.022
Table 4.7: Comparison of the expected and measured single-polarization optical efficiency. See the text for a description of how the different contributions to the expected efficiency are determined. The values quoted for the measured efficiency are the median and median absolute deviations over resonators of a given band on the detector arrays in the A2 and B2 positions.
Expected Efficiency Measured
Efficiency (ηph×ηopt,ant)
Measured / Expected Band Phonon Absorption Microstrip Antenna Lyot Stop Filters Total
0 0.60 0.88 0.88 0.74 0.28 0.74 0.071 0.083±0.013 1.17±0.18
1 0.50 0.88 0.83 0.70 0.51 0.76 0.099 0.125±0.015 1.26±0.15
2 0.46 0.88 0.79 0.78 0.68 0.69 0.117 0.108±0.014 0.92±0.12
3 0.43 0.88 0.75 0.71 0.76 0.61 0.093 0.074±0.022 0.79±0.24
the direct absorption by a factor of'1.6, which is less than the expected factor of 2, but still represents a significant improvement. The hot/cold results for the dark resonators are used to correct the hot/cold results for the antenna coupled resonators using the procedure outlined in Section 3.2.3. This enables extraction of the optical efficiency and excess loading of the antenna.
We now compare the measured optical efficiency to the expected optical efficiency based on the known sources of loss in the MUSIC instrument. Table 4.7 tabulates the known sources of loss. We associate an expected efficiency to each, which is estimated from either a direct measurement, analytical calculation, or simulation:
Phonon Refers toηph. The quoted values are taken from the simulation of Guruswamy et al. [87]. The origin ofηphand a description of the simulation are given in Section 2.2.2.
Absorption Refers to the fraction of the power incident on the MKID that is absorbed by the MKID. The quoted values are the result of an analytical calculation [161]. This calculation accounts for two effects, which have opposing dependencies on the resistivity of the Al section. First, as the resistivity of the Al section increases, the length scale for absorption of light from the overlapping Nb/Si3N4microstrip becomes smaller, resulting in an improved absorption efficiency. Second, as the resistivity of the Al section increases, the impedance mismatch between the Al section and the Nb portion of the microstrip increases, resulting in reflection and a reduced absorption efficiency. The calculation assumes that the Al has a sheet resistance of 0.22Ω/, which is based on direct measurements made at 4 K.
Microstrip Refers to dielectric loss of the microstrip that carries the light collected by the antenna to the MKID. The loss tangent of the Si3N4 dielectric at millimeter-wave frequencies was measured using a set of “loss test devices” on an engineering-grade detector array, Device 9a. The loss test device is designed as follows. Light collected by an antenna is sent through a 3 dB microstrip splitter; half of the power is sent directly to a “reference” MKID and the other half is sent over a long run of microstrip before terminating in a “loss” MKID. The difference in the length of microstrip between the loss and reference MKID is 41.4 mm. The hot/cold analysis is carried out on both the loss and reference MKID.
The ratio of the optical efficiency of the loss MKID to that of the reference MKID yield an estimate of the dielectric loss in the excess run of microstrip, which can then be converted into a dielectric loss tangent. We find that on average the loss MKID has an optical efficiency that is 0.26 times that of the reference MKID. We have measured the band center of the loss test devices to be 330 GHz via FTS.
Hence, the loss tangent of Si3N4is 1.6×10−3. This results in the microstrip efficiencies quoted in Table 4.7 for the 8.4 mm length of microstrip used in the actual detectors.
Antenna Refers to the efficiency of the phased array of slot dipole antennas. It is calculated by applying the method of moments to an infinite array of infinite long slots. This accounts for feed efficiency, radiation efficiency, and transmission through the silicon and AR coating. It does not account for losses
to substrate modes, which is expected to be an∼10% effect. It also does not account for inefficiency due to the fact that the actual slots have finite length and the impedance varies near the ends, which is expected to be another∼10% effect that will be largest for the lower frequency bands.
Lyot Accounts for the loss due to the truncation of the beam at the Lyot stop. It is estimated using Zemax simulations of the MUSIC optics [138].
Filters Accounts for the loss and reflections of the dielectric, metal-mesh, and infrared shader filters. The loss of each filter is estimated using the methods and references outlined in Sayers et al. [138]. The reflections at the interface of each filter is estimated via simulation.1
The product of these efficiencies is presented in theTotalcolumn of Table 4.7. We expect that the MUSIC in- strument will have single-polarization optical efficiencies between 7% and 12%, depending on the observing band.
In general, the optical efficiencies inferred from hot/cold are in good agreement with the expected optical efficiencies. There does appear to be a slight band dependent discrepancy. In Band 0 and Band 1 the measured efficiency is larger than expected, whereas in Band 2 and Band 3 the measured efficiency is smaller than expected. The quoted uncertainties are simply the dispersion observed across the detectors of a given band.
There is also systematic uncertainty in the measured values that arise from our uncertainty in the assumed values of the recombination coefficient and the thickness of the Al section. This systematic uncertainty is not included in the quoted uncertainties. However, it should effect all bands approximately equally, and therefore would not explain the band dependent discrepancy. The true efficiencies would be 30% greater than the quoted values if zero Al is etched away during fabrication instead of the assumed 15 nm. The true efficiencies would be 50% less than the quoted values if 30 nm of Al is etched away instead of the assumed 15 nm and if the recombination coefficient is 7.1µm3sec−1instead of the assumed 9.4µm3sec−1. Note that the
+30%
−50%systematic errors correspond to the absolute boundaries of what we believe are reasonable values for the recombination coefficient and thickness. Without independent measurements of the recombination coefficient and thickness of the MKIDs employed in MUSIC, it is difficult to determine the overall normalization of the band dependent optical efficiency to better than approximately 50% accuracy.