HEMT (4 K)
5.6 Method to reduce the noise
From Eq. 5.80, the noise scaling is predicted to be I3m(t, sr, V) ∝ s−r2−γ ∼ s−r1.55 (at fixed V), which agrees surprisingly well with the measured s−r1.58 scaling. We also investigated the case for TLS located on the exposed substrate surface, and found thatF3g has almost identical scaling (γ ≈ −0.45) as F3m. While we still cannot say whether the TLS are on the surface of the metal or the exposed substrate, we can safely rule out a volume distribution of TLS fluctuators in the bulk substrate; this assumption yields a noise scaling of ∼s−r1.03, significantly different than that measured.
In summary, the scaling of the frequency noise with resonator power and CPW geometry can be satisfactorily explained by the semi-empirical model developed in Section 5.4.6 and with the as- sumption of a surface distribution of independent TLS fluctuators. These results allow the resonator geometry to be optimized, which will be discussed in the next section. Had we known the exact E~ field distribution and the exact TLS distribution for our CPW resonators, we would be able to derive the noise coefficientκ(ν, ω, T) as we did for the SiQ2microstrip experiment discussed earlier.
Unfortunately, the two parameters, the edge shape and the thickness of the TLS layer, required for calculating κ(ν, ω, T) are not easily available. However, they are expected to be common among resonators fabricated simultaneously on the same wafer, and more or less stable for resonators fab- ricated through the same processes. Since we have shown that the ratio of |E~|3 integral between two resonator geometries is insensitive to the edge shape, we can still predict the scaling of the noise among different resonator geometries[74].
1 2
Figure 5.30: An illustration of the two-section CPW MKID design. Quasiparticles are generated and confined in the effective sensor area indicated by the red strip.
2 1
Figure 5.31: An illustration of the MKID design using interdigitated capacitor. Quasiparticles are generated and confined in the effective sensor area indicated by the red strip.
the coupler end to benefit from the noise reduction, but a narrower section (with center strip width s2, gapg2, and lengthl2) at the low-|E~|shorted end to maintain a high kinetic inductance fraction and responsivity. Meanwhile, we can make the section 1 CPW from a higher gap superconductor (e.g., Nb) and section 2 from a lower gap superconductor (e.g., Al), to confine the quasiparticles in section 2. To maximize the noise reduction effect and the responsivity, we should also makel1≫l2. In the example design as shown in Fig. 5.30, we haves1/s2=g1/g2= 4. According to thes−r1.6 noise scaling, this detector design is expected to give 9 times lower frequency noise and therefore 3 times better NEP as compared to the conventional one-section CPW withs2 andg2.
5.6.1.2 A design using interdigitated capacitor
The wider geometry section in the two-section CPW design can be replaced by a interdigitated planar capacitor section, as shown in Fig. 5.31. Such an interdigitated design makes the resonator more compact and easier to fit into a detector array where the space is limited. The strips and gaps in the interdigitated capacitor should be made as wide as is allowed by the space in order to maximize the noise reduction effect. Because the dimension of the capacitor (l1∼1 mm) is designed to be much smaller than the wavelengthλ >10 mm, the voltage distribution on the interdigitated capacitor structure is almost in phase and such a structure indeed acts as a lumped-element capacitor C′. The length of the shorted sensor strip in section 2 is also much smaller than the wavelength, so the sensor strip acts as an inductor with inductanceL′ =Ll1, whereL is the inductance per unit length of the CPW in section 2. The entire structure shown in Fig. 5.31 virtually becomes a parallel RLC resonant circuit and can be conveniently described by a lumped-element circuit model.
5.6.2 Removing TLS
An obvious way of reducing excess noise is to remove the TLS fluctuators from the resonator, partially or completely.
5.6.2.1 Coating with non-oxidizing metal
If the TLS are in the oxide layer of the superconductor, coating the superconductor with a layer of non-oxidizing metal (for example, Au) may get rid of some of the TLS on the metal surface and reduce noise. However, it can not remove all the TLS because the superconducting film will still be exposed to air and form oxides at the edges where they are etched off. Because the electric field strength is usually peaked at these edges, the noise contributions from these remaining TLS, according to the |E~|3 weighting, are still significant. EM simulation shows that this method may only moderately reduce the noise by a factor of a few.
5.6.2.2 Silicides
The surface oxide can only be avoided if the superconducting film is not exposed to air. This is almost impossible for standard lithographed planar structures but may be possible by using superconducting silicides (such as PtSi[75], CoSi[76]). These silicides are made by ion implantation of metal into silicon substrate. With this process, for example, one can bury a entire CPW into the crystalline Si up to∼100 nm deep beneath the surface. One can bury it even deeper by regrowing crystalline Si on the surface. Because the crystalline structure of Si will not be destroyed and no amorphous material will be created in these processes, the devices made from these silicides are expected to be free of TLS fluctuators and excess noise.
5.6.3 Amplitude readout
As has been shown earlier in this chapter, no excess noise is observed in the amplitude direction and the amplitude noise, set by the noise temperature of HEMT, can be orders of magnitude lower than the phase noise at low noise frequencies. Therefore, using amplitude readout may avoid the excess noise and in some cases give better sensitivity.
Recall from Chapter 2 and 4 that a change in the quasiparticle will cause a change in both the real (σ1) and imaginary (σ2) part of the conductivity, resulting in an IQtrajectory that is always at a nonzero angleψ= tan−1(δσ1/δσ2) to the resonance circle. Calculation from Martis-Bardeen’s theory shows that tanψ= 1/4∼1/3 for the temperature and frequency range that MKIDs usually operate in. This means as soon as the phase noise exceeds the amplitude noise (HEMT noise floor) by about a factor of 10 (in power), amplitude readout may yield a better NEP than the phase readout.
0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0
0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0
T im e ( 4!s )
Pulse height
Figure 5.32: Detector response to a single UV photon event. The data is measured from a 40 nm Al on sapphire MKID illuminated by monochromatic UV photons (λ= 254 nm) at around 200 mK.
The quasi-particle recombination time is measured to be 20µs. The inset shows the resonance circle and the pulse response in the IQ plane. In the zoom-in view of the pulse response, one can identify the pulse and the noise ellipse. The angle between the average pulse direction and the major axis of the noise ellipse is 15◦.
Fig. 5.32 shows the measured detector response to a 254 nm UV photon. From the average pulse trajectory and the major axis of the noise ellipse, we determine ψ ≈15◦. Applying the standard optimal filtering analysis to these data, we derived the NEP for both the phase and amplitude readout, which is plotted in Fig. 5.33. We see that amplitude NEP is a factor of 4 lower than the phase NEP at low frequency (below 10 Hz). At high frequency (above 5 kHz), the phase NEP becomes better than the amplitude NEP again. To take advantage of the signal in both directions, one can analyze the data using a two-dimensional optimal filtering algorithm. It can be shown that
100 101 102 103 104 105 10−17
10−16 10−15
NEP [W⋅ Hz−1/2 ]
Freqeuncy [Hz]
NEP Phase NEP Amplitude NEP 2D
Figure 5.33: NEP calculated for the phase readout (blue), amplitude readout (green), and a combined readout (red)
the two-dimensional NEP is given by
NEP−2D2= NEP−pha2 + NEP−amp2 (5.89) which is indicated by the lowest curve in Fig. 5.33.
Chapter 6
Sensitivity of submm kinetic inductance detector
In this chapter, we will discuss the sensitivity of submm MKIDs, as an example of applying the models and theories of superconducting resonators developed in the previous chapters.
As the first stage of the detector development, these submm MKIDs are to be deployed in the Caltech Submillimeter Observatory (CSO), a ground-based telescope. For ground-based observa- tions, it is inevitable that the detector will be exposed to the radiations from the atmosphere and have a background photon signal. Once the intrinsic noise of the detector is made smaller than the shot noise of this background photon signal, the sensitivity of the detector is adequate. This requirement is called background limited photon (BLIP) detection.
One of the important questions to be answered in this chapter is whether our submm MKIDs can achieve the background limited photon detection on the ground, or in other words, whether the intrinsic detector noise (g-r noise, HEMT amplifier noise, and TLS noise) is below the photon noise of the background radiation from the atmosphere.