Microwave Kinetic Inductance Detectors

Many of the good ideas dealing with the cryogenics and thinking about the data are his. This is strong evidence that the substrate is the cause of the noise, as shown in Chapter 8.

Introduction to Low Temperature Detectors

When a photon is absorbed in the superconductor, the current required to maintain the elevated strip temperature drops. The last column, TheoreticalδE, shows how the energy resolution of the device changes to detect a single photon.

Microwave Kinetic Inductance Detectors

The concept of noise equivalent power (NEP), a measure of detector sensitivity, will be discussed at length in Section 7.1.4.6. This concept takes advantage of recent dramatic advances in the performance of cryogenic microwave HEMT (High Electron Mobility Transistor) amplifiers, which provide sub-10 K noise temperatures in multi-gigahertz bandwidths and now operate at frequencies up to several hundred gigahertz [ 37 ].

Figure 1.1: An illustration of the detection principle.

Scientific Motivation

Astronomy

The second row contains simulations with all attenuation and confusion factors, including cosmic variance. This will allow us to understand the baryon density of the universe and the state of the IGM as a function of time.

Figure 1.3: An image of the intensity and polarization of the cosmic microwave background radiation made with the Degree Angular Scale Interferometer (DASI) [40]

X-ray Microanalysis

They will investigate the energy generation mechanisms of quasars (Figures 1.9 and 1.10) and black holes with stellar mass. The figures are snapshots of a simulated outburst near a supermassive black hole at two different times.

Dark Matter Detectors

One promising class of dark matter candidates is known as Weakly-Interacting Massive Particles (WIMPs). The Cold Dark Matter Search (CDMS) currently uses 4 TES sensors to measure the phonons deposited in the target crystal.

Figure 1.11: Current constraints and allowed parameter space for SUSY WIMPs. Constraints: CDMS 2000 limit [72]; EDELWEISS 2002 limit [73]; DAMA 2000 3σ allowed region [74]

The Surface Impedance of Superconductors

In the dirty limit, the electron mean free path lmf p is much smaller than the magnetic penetration depth λ and the coherence length ξ0 = ¯hvf/π∆(0), where vf is the Fermi velocity of the electrons. 4πne2 is much smaller than the coherence length, where m is the mass of an electron, e is the electron charge, and n is the density of conduction electrons.

Photon Detection

Although the changes in δZs may be small, we can make it a very sensitive measurement using a resonant circuit as shown in Figure 1.1b. By combining responsiveness with knowledge of how well we can measure phase in a given time period (known as phase noise, which can be intrinsic to the device or related to the way we generate and read out the signal) we can determine the noise equivalent power , signal-to-noise ratio and dynamic range of an MKID.

Figure 2.1: Values of σ 1 /σ n , [σ 2 (0)−σ 2 (T )]/σ n , and σ 2 /σ 1 derived from the Mattis-Bardeen integrals for a 320 nm thick aluminum film (T c = 1.175 K) as a function of T c /T

Resonator Theory

Parallel LC Resonant Circuit

The averaging is performed over one cycle of the oscillation, and the factor of two accounts for the fact that on average half the energy is stored in the inductor and the other half in the capacitor. Thus, the full width at half maximum (FWHM) of the power transmission curve is given by.

Half Wave Resonator

Thus, in terms of the voltage V at the end of the line, the energy is stored in the capacitance of the transmission line. 2.27), where the average calculation is carried out as before over one cycle of the oscillation. The additional factor of 1/2 is included for the spatial average of the standing voltage wave over the length of the wire.

Figure 2.3: A transmission line resonator with series capacitors for input and output coupling

Quarter Wave Resonator

At that frequency, the transmission line section appears inductive and sets the large capacitive reactance of the coupling capacitor. The interesting solution is the lower frequency one, because at the higher solution, which is closer to ω1/4, the real part of the impedance of the transmission line section is very large and does not load the through line.

Figure 2.6: A quarter wave transmission line resonator shown represented schematically with coaxial transmission lines.

Calculating Resonator Parameters

We have included a factor ofα that represents the fraction of the total inductance of the transmission line that is contributed by the kinetic inductance. This low temperature limit of the resonator quality factor Q(0) results from energy leaking out of the resonator as shown in Equation 2.26.

Figure 2.7: The amplitude and phase of a microwave probe signal transmitted past a quarter wave resonator near resonance

Resonator Responsivity

After a little math, it is possible to calculate the change in the surface impedance of the transmission line at resonance due to a localized injection of quasiparticles into a quarter-wave resonator δLn(T). The general result is that the response of the resonator to the injection of quasiparticles is position dependent, weighted by the square of the current distribution in the transmission line.

Choosing an Architecture

Radiation above the gap frequency will break Cooper pairs in the superconductor and result in a lossy transmission line. The gap frequency of aluminum is 90 GHz, which means that this is the lowest frequency that an aluminum MKID can detect.

Figure 3.2: Coupling millimeter or submillimeter photons to a quarter wave CPW resonator may be achieved by using an antenna to absorb the incoming radiation and send it down a niobium microstrip

Frequency Domain Multiplexing

The top inset shows a magnified view of the coupling region, and the bottom inset shows the corresponding circuit. resonator section, with a total length of 3 mm and resonant frequency around 10 GHz. The lithographic precision of the resonator length determines how precisely each resonant frequency is tuned.

Figure 3.4: A lumped element microstrip resonator fed with a CPW transmission line A. The overlap B serves as the coupling capacitor

Design Parameters

CPW Geometry
Coupling
Radiation Loss
Quasiparticle Lifetimes
Quasiparticle Diffusion and Trapping
Material Choice
Strip Detectors
Other Design Parameters

The legend indicates the length of the CPW line running parallel to the supply line. At each end are the meandering resonators (white) - the length of the resonators decreases towards the top of the device.

Figure 3.6: A photograph of an array of elbow couplers designed in Section 3.3.2 with dimension specified in Figure 3.5

Theoretical Noise Sources

Generation-Recombination Noise

Fano Noise

These calculations were performed with an IR wavelength of 2 µm, optical wavelength of 0.4 µm, UV wavelength of 0.12 µm and X-ray energy of 6 keV. From this formula we can calculate the maximum energy resolution for a given photon energy and absorber gap.

Figure 3.16: Expected generation-recombination noise from a 3 µm center strip, 6 GHz aluminum on sapphire, 220 nm thick resonator with τ qp = 200 µs as a function of temperature.

Calculating Responsivity

Test Wafer Layout

Optical/UV/X-ray Array Wafer Layout

Array Fabrication

Kelvinox Description

Device Mounting

The wire connections from the side of the channel to the ground plane on the chip are designed to suppress unwanted waveguide transmission modes that could cause excessive microwave leakage through the box. The left axis shows the magnetic permeability µ/µ0 at 4 mA/cm and the temperature is Celsius.

Figure 4.4: A aluminum on silicon device from the test mask mounted in a sample box. The box is 1” by 1” by 0.225”

Device Isolation

Magnetic Shield

This should be considered an upper limit, as our actual shield is not spherical, is perforated in several places for cables and thermal connections, and may suffer from magnetic saturation effects depending on the magnitude and frequency of the applied magnetic field. Measurements show that the filter has good transmission at low frequencies, but the high cutoff frequency (50 GHz) makes the stopband attenuation difficult to measure with our current instruments.

Figure 4.7: The design of the 50 GHz low pass filter.

HEMT Amplifier Biasing

Temperature Measurement and Control

This system is designed to have low internal noise and the ability to improve on a readout for an average sized group. This chapter will explain the details of the readout system and the characterization performed on it.

Readout System Overview

We start by exploring the microwave system, which includes all the components before the output of the IQ mixers. We will then move on to the low frequency system, which follows the signal path from the IQ mixers output to the analog to digital converter.

Microwave System Description

Variable Attenuators
Phase Noise Monitoring
Carrier Suppression
Rubidium Frequency Standard
A/D Conversion
GPIB Control
Computer

After the amplifiers, the signal is sent to a directional coupler. The linked port provides a copy of the signal at -20 dB, which is available for diagnostics. This results in a total voltage gain of 3.5 from the output of the IQ mixer to the digitizer.

Figure 5.2: The circuit diagram of an IQ mixer.

Microwave System Characterization

Microwave Synthesizers

Bitmask is an eight bit number and turns on the switches where there is a binary 1. Channel=1 sets the attenuation for Anritsu Synth 1, and Channel=2 sets the attenuation for Anritsu Synth 2.

Microwave Amplifiers

One-Box, Ultra-Clean RF and Microwave Signal Solutions

MHz, these synthesizers utilize Direct Digital Synthesis (DDS) techniques to achieve ultra-fine frequency

MHz to 2.2 GHz, the new Digital Down Converter (DDC) is available offering ultra-low SSB phase noise

GHz, Anritsu uses patented techniques that allow us to achieve the best possible phase noise performance

Cleaner Phase Noise Means More Accurate Measurements

IQ Mixers

Combining the data from Figure 5.8 with the measured output impedance of the IQ mixer (140 Ohm) allows us to calculate the conversion loss of the mixer. The power spectra of the fluctuations at the output of the IQ mixer, SIQ, can be written as.

The Low Frequency System Characterization

Amplifier and Filter Board
Noise Analysis Routines
Characterization of Readout Noise

The lower curve of Figure 5.11, shown in black, is the noise of the IQ mixer times the gain of the amplifier board. Signal noise with room temperature microwave amplifiers on is shown in red.

Figure 5.9: In order to check that we are correctly calculating the power spectrum, analog signals from a Stanford Research DS360 Low Distortion Function Generator was sent into both the ICS-145 board and a Stanford Research Low Frequency Spectrum Analyzer

Future Readout Schemes

Single Board RF Signal Generation and Recovery
Integrated Digitization and Analysis

This is only practical if provision is made to measure the DC values at the IQ outputs in some other way. The initial data reduction consists of three main areas: adjusting the IQ resonance sweeps to obtain resonator parameters, adjusting the resonator parameters to obtain fundamental material parameters, and calculating noise spectra.

Figure 5.13: A custom two channel single RF board readout using microwave integrated circuits developed for the wireless industry

Fitting Resonator Parameters

The green cross is the calculated center of resonance, and the orange circle is where the derivative of the distance between IQ points reaches a maximum – this should correspond to the resonant frequency of the device. The first term is derived from Equation 2.43, the second term is an offset to move the resonance feature in the complex plane, and the last two terms are leakage terms.

Figure 6.1: An example of the resonance fitting function’s ability to match difficult resonator data.

Deriving Material Parameters

Noise Analysis

Transition Temperature
Quality Factors
Derived Material Parameters
Noise

The phase angle θ is defined from the center of the resonance circle with a range of 0 to 2π. The highest readout powers (shown in the darkest colors) are well above the saturation power of the resonator.

Table 7.1: Measured Q and f 0 of a 320 nm thick aluminum on high purity silicon B0 device from the test mask

Thin Aluminum on Silicon Resonator Results

Transition Temperature
Quality Factors
Derived Material Parameters
Noise

Q in figure 7.30, and at a readout effect just below the saturation effect of the individual resonator in figure 7.31. The phase noise in relation to the output power for resonator 1 from the 40 nm B0 device is depicted in Figure 7.32.

Figure 7.23: The resonant frequencies of the resonators on the 40 nm thick Al on Si B0 device

Comparison of 320 and 40 nm Data

The Variation of Resonator Parameters with Width

Frequency Accuracy
Quality Factors
Noise

This is not a particularly good way to compare the resonators, as their different geometries and quality factors result in very different electromagnetic fields in the substrate, which we have previously shown to be a dominant effect on the noise of the 3 µm center strip resonators. The cutting process damaged many of the devices, and the W0 device was the most interesting of the remaining devices.

Table 7.7: Measured Q and f 0 of a 320 nm thick aluminum on silicon K0 device from the test mask.

Frequency Accuracy

The W0 device, made using 205 nm aluminum on sapphire by Rick LeDuc at JPL, was cooled in our refrigerator on April 15, 2004. It is the first device we have tested made on sapphire that remained after to the Herschel project.

Table 8.1: Measured Q and f 0 of a 205 nm thick aluminum on sapphire W0 device from the test mask

Quality Factor

Transition Temperature

Derived Material Parameters

Noise

Frequency Noise
Noise Power Dependance
Phase Change per Quasiparticle
Saturation Energy

Note that the slope of the power dependence (blue line) is almost identical to the slope of the silicon data in Section 7.1.4.2. This is further evidence that the source of the excess noise is the substrate.

Figure 8.4: A comparison of the phase noise of resonator 2 from the 320 nm Al on Si B0 device and resonator 1 from the 205 nm Al on Sapphire W0 device

Effective Dielectric Constant

Quality Factor

Derived Material Parameters

Noise

Frequency Noise
Noise Power Dependance
Frequency Noise Comparison
Saturation Energy

In Figure 9.6, we plot the frequency noise at -74 dBm, the same data set, scaled by s. Q in Figure 9.7 and at a reading power just below the saturation power of the individual resonator in Figure 9.8.

Figure 9.5: A comparison of the phase noise of the resonators from the etched C1 device

Resonator Parameters

The devices on the left side of the device are in black and the devices on the right side are in red. The total standard deviation of all points of the best fit line is 5.2 MHz, but if you look at the left and right sides of the device independently, the agreement with the expected values is much better.

Noise

Noise Equivalent Power

We can now assemble a map of the resonator to determine which strips can act as strip detectors. The noise equivalent power of the optical array resonator device is slightly lower than the corresponding device from the test mask.

Figure 10.2: The measured Q and resonance frequency of the S3.50T-6.20-1Q6-32x32 device

X-ray Detection

The resonant frequency of the device is determined by its length and the dielectric constant of the substrate. The maximum read power is a function of Q and the thickness of the superconducting film used in the resonator.