Cleaner Phase Noise Means More Accurate Measurements
7.2 Thin Aluminum on Silicon Resonator Results
7.2.4 Noise
Following the procedure outlined in Section 7.1.4 we can analyze the noise of these thin resonators.
We will limit ourselves to the resonators with lower coupling Qs, and omit resonator 3 due to problems in the data collection. This leaves resonators 1,2,4,5, and 6 from Table 7.4.
We can perform fits to the phase noise spectrum to help understand the noise, as shown in Figure 7.28 and Table 7.5. The noise roll-off frequency does not fit as well as for the thick data, but this can be understood by looking at the fits. The thin data tends to have a flatter mid-frequency region than the thick data, leading to poor fits.
7.2.4.1 Frequency Noise
We can perform the same transformation as in Section 7.1.4.1 to derive the frequency noise for these resonators. We plot the frequency noise at -104 dBm in Figure 7.29, the same data set scaled by
101 102 103 104 105 Frequency (Hz)
−80
−70
−60
−50
Sθ(f) (dBc/Hz)
Q = 153548 Q = 214991
Figure 7.28: The phase noise fits of resonators from the 40 nm thick Al on Si B0 wafer measured at a readout power of -104 dBm. Quality factors of these resonators are listed on the right side of the plot.
√Q in Figure 7.30, and at a readout power just below the individual resonator’s saturation power in Figure 7.31.
The results of this procedure is a nearly identical result to those seen for the thick film devices, showing that the frequency noise of resonators depends on stored energy in the resonator, and not onQ. Section 7.3 will compare the noise of resonators from the thick and thin film devices.
7.2.4.2 Noise Power Dependance
The phase noise versus readout power for resonator 1 from the 40 nm B0 device is plotted in Figure 7.32. It shows a very similar trend to the thick data, where the phase noise drops as the readout power and the stored energy in the resonator increases.
7.2.4.3 Phase Change per Quasiparticle
One of the most interesting results from the thin film resonators is a direct comparison of the phase change per quasiparticle in the center strip to a resonator of identical geometry from the thick film device. From Figure 7.34 and Tables 7.3 and 7.6 we can look up dθ/dNqp for the thick and thin resonator 2. Resonator 2 from the 320 nm thick devices hasQ= 48095 anddθ/dNqp= 7.4×10−8. Resonator 2 from the 40 nm thick devices hasQ= 49333 anddθ/dNqp= 6.7×10−6.
Dividing the values ofdθ/dNqpgives a responsivity 91 times greater for the thin film for a given Q. Taking out the change in volume by a factor of 320/40 = 8 and the change in the kinetic
101 102 103 104 105 Frequency (Hz)
0.1 1.0 10.0 100.0 1000.0 10000.0
Sf(f) (Hz2 /Hz)
Q = 61506 Q = 48333 Q = 151607 Q = 153548 Q = 214991
Figure 7.29: The frequency noise of resonators from the 40 nm thick Al on Si B0 device at a readout power of -104 dBm. TheQindicated in the legend is theQderived from a fit at this power level.
101 102 103 104 105
Frequency (Hz) 0.1
1.0 10.0 100.0 1000.0 10000.0
Sf(f) (Hz2 /Hz)
Q = 61506 Q = 48333 Q = 151607 Q = 153548 Q = 214991
Figure 7.30: The frequency noise of resonators from the 40 nm thick Al on Si B0 device at a readout power of -104 dBm scaled by the√
Qdivided by the√
Qof the lowestQresonator. TheQindicated in the legend is theQderived from a fit at this power level.
101 102 103 104 105 Frequency (Hz)
0.1 1.0 10.0 100.0 1000.0 10000.0
Sf(f) (Hz2 /Hz)
Q = 48333 Q = 135178 Q = 153548 Q = 220510
Figure 7.31: The frequency noise of resonators from the 40 nm thick Al on Si B0 device at a readout power just below the saturation readout power of each individual resonator. TheQindicated in the legend is theQderived from a fit at the power level the noise data was taken at.
101 102 103 104 105
Frequency (Hz)
−80
−70
−60
−50
Sθ(f) (dBc/Hz)
−100 dBm −102 dBm −104 dBm −106 dBm −108 dBm −110 dBm
Figure 7.32: The phase noise of resonator 1 from the 40 nm thick Al on Si B0. The readout power ranges from -100 dBm to -110 dBm in steps of 2 dBm.
−6000 −5000 −4000 −3000 −2000 −1000
−4000
−3000
−2000
−1000 0 1000
Figure 7.33: The IQ curves of a resonator 2 from the 40 nm thick Al on Si B0 device. The quality factor of this resonator is Q = 48,333. The resonance shrinks and shifts frequency as the device is warmed from 120 mK to 320 mK. The green cross is the resonance center from the fits to the lowest temperature resonance curve. The black circles are points of constant frequency (the resonant frequency of the lowest temperature resonance curve).
inductance fraction ofα=.47/.055 = 8.5 leaves a factor of 1.3 that is probably due to the increase of the gap as the film becomes thinner. This effect can be estimated using Equation 2.58.
Figure 7.34 shows the responsivity of resonator 2. The estimated responsivity of the device is shown in green, and is an excellent match to the actual data despite the problems we expected applying bulk aluminum calculations to this thin film data.
7.2.4.4 Quasiparticle Lifetimes
We can take data on the quasiparticle lifetimes using the method of Section 7.1.4.4. For this film thickness we get a quasiparticle lifetime of approximately 65 microseconds, as seen in Figure 7.35.
7.2.4.5 Saturation Energy
We can calculate the saturation energies using the methods of Section 7.1.4.5. Results range from 10–47 eV as shown in Table 7.6. These thin film devices saturate at very low powers suitable for optical/UV detectors.
0 5.0•105 1.0•106 1.5•106 2.0•106 Number of Quasiparticles in Center Strip
0 50 100 150
Phase Shift (degrees)
Figure 7.34: The phase shift vs. quasiparticle number at constant frequency of resonator 2 from the 40 nm thick Al on Si B0 device. Quality factors of this resonator isQ= 48,333. The red line is the fit to the data used to derivedθ/dNqp.
150 200 250 300
T (K) 0
20 40 60 80
Quasiparticle Lifetime (µs)
Figure 7.35: The measured quasiparticle lifetimes in the 40 nm thick B0 device as a function of temperature.
101 102 103 104 105 Frequency (Hz)
10−16 10−15 10−14
NEP (W Hz−1/2)
Q = 59732 Q = 48333 Q = 135178 Q = 153548 Q = 220510
Figure 7.36: The noise equivalent power (NEP) of resonators from the 40 nm thick Al on Si B0 device. The NEPs are calculated for a readout power just below the saturation value.
7.2.4.6 NEP
We can calculate the NEP and energy resolution using the procedure of Section 7.1.4.6 at readout powers just below the saturation power of the individual resonators results in Figure 7.36 using τqp= 65µs derived in Section 7.2.4.4.
The NEPs for the thin film resonators are lower than the thick film resonators by a factor of∼10.
The improvement in NEP was not as great as the improvement indθ/dNqp because the much lower saturation power of these resonators resulted in higher frequency noise as shown in Section 7.2.4.2.
Since the responsivities are up by a factor of∼90 the dynamic range has been reduced by about 90/10 = 9. This is acceptable for an optical/UV device because the quasiparticle creation (Fano) statistics limit the energy resolution as discussed in Section 3.4.2. The signal to noise ratios that we see in the lowQresonators is close to state-of-the-art for superconducting optical detectors.
These resonators needed very low readout powers to avoid saturation. As we will see in Chapter 8, resonators on sapphire appear to be able to deal with much higher readout powers than resonators on silicon. Since the phase noise goes down as the readout power goes up on both silicon and sapphire (Section 9.4.2), we expect thin films on sapphire to have significantly better performance.
135178 -103 1.4×10−5 22 5.3×10−14 1.2×10−16 3.9
153548 -105 1.3×10−5 23 5.7×10−14 1.0×10−16 3.7
229510 -107 2.9×10−5 10 2.5×10−14 7.1×10−17 2.4
Table 7.6: Calculated saturation energies, minimum values of the NEP, and energy resolution for the resonators discussed in this section taken at a readout power just below the saturation power.