Readout and characterization system for kinetic inductance detectors (KID) of the MUSCAT project.

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Readout and characterization

system for kinetic inductance

detectors (KID) of the MUSCAT

project.

by

Marcial Becerril Tapia

Thesis submitted in partial fullfillment of the

requirements for the degree of

MAESTRO EN CIENCIAS en la especialidad de

ASTROF´ISICA

at the

Instituto Nacional de Astrof´ısica, ´

Optica y

Electr´onica

December 2019

Tonantzintla, Puebla

Advised by:

PhD. Abraham Luna Castellanos

Researcher - INAOE

PhD. Edgar Castillo Dom´ınguez

Project Lead - SRON

PhD. Sam Rowe

Research Associate - Cardiff University

c

INAOE 2019

The author hereby grants to INAOE permission to

reproduce and to distribute publicly paper and

electronic copies of this thesis document in whole or

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Readout and characterization system for kinetic inductance

detectors (KID) of the MUSCAT project.

por

Marcial Becerril Tapia

Ingeniero en Mecatrónica

Tesis presentada para obtener el grado de

Maestro en Ciencias en la Especialidad de Astrofísica

en el

Instituto Nacional de Astrofísica, Óptica y Electrónica

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A mis padres J. Carmen y Sandra (Mary), y hermanos Ale, Gabriel y Liliana, por su amor, consejos y apoyo incondicional, y muy cariñosamente al pueblo de México, a quien agradezco profundamente la educación que me brindó.

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Agradecimientos

Este trabajo es el resultado de la participación directa e indirecta de una plétora de asombrosas personas, que con sus conocimientos, consejos, experiencias y aliento cristalizaron este sueño en toda una realidad. Éste es su trabajo.

Quiero comenzar por agradecer a mi padre, Carmelo, por enseñarme a vivir a través de sus historias, por inculcar en mí, la disciplina y el sentido de la responsabilidad, y sobre todo por apoyo incondicional en todo lo que me he propuesto en la vida aunque no siempre estuviese del todo convencido. A mi amada madre, Sandra, por todo su amor y cariño, por enseñarme el valor de la honestidad, por su admirable dedicación y fortaleza para que yo y mis hermanos no tuvieramos que preocuparnos nunca por otra cosa que los estudios, por esas noches que se desvelaba con nosotros hasta que terminabamos nuestras tareas sólo para acompañarnos, mil gracias mamá.

También agradezco a cada uno de mis hermanos, Alejandra, Gabriel y Liliana, por todos los momentos vividos y el apoyo, en todos los sentidos, que representan.

A mis amigos y también colegas Rodrigo y Mario, unas magníficas personas y profesionistas, con quienes tuve la oportunidad de compartir la formación profesional, a ellos agradezco todas las vivencias, consejos y sobre todo su amistad.

A mi asesor Abraham Luna, por sus valiosísimos consejos en el plano profesional y personal. Gracias por todas sus enseñanzas, por sus charlas (que a veces se prolongaban hasta muy tarde), por esa manera tan única de transmitir con tanta pasión y entusiasmo la astronomía, sembrando en todos sus estudiantes, incluyéndome, el amor por la ciencia; sin duda, uno de los mejores docentes y divulgadores de la ciencia que conozco.

A mi asesor Edgar Castillo, por compartirme algunos de sus vastos conocimientos y experien-cias profesionales en el campo de la instrumentación astronómica. Le agradezco inmensamente todo su apoyo intelectual y todas las oportunidades académicas que me presentó, pero sobre todo, con mucho cariño le agradezco su apoyo y consejos personales que tantas veces nos com-partía durante aquellas charlas de café, y la gran oportunidad de conocer al gran ser humano que es.

Very affectionately to Sam Rowe, for the warm welcome in Cardiff and his invaluable support to make this new city my home. For all of his invaluable knowledge and advice, without which this work would not have been possible, for all those times in which always regardless of all his occupations, he devoted a part of his time to explain me any topic or resolve my doubts (sometimes inopportunes) with its particular and pleasant style. However, what I appreciate most is having given me the opportunity to meet him, in addition to a leading scientist and professor, a great person.

A Salvador Ventura, por compartir sus vivencias en la investigación como recién estudiante

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egresado del doctorado, verdaderos consejos para el campo profesional con quien generacional-mente comparto afinidad. Sobre todo agradezco de corazón su apoyo y grata companía en Cardiff, que hizo mucho más suave la asimilación cultural en un país completamente nuevo para mí. Siempre recordaré con mucho cariño su parábola de "línea", aunque no puedo asegu-rarle que no la cruzaré.

A mi buen amigo José Miguel, por sus enseñanzas, por su apoyo constante y sus sugerencias a éste trabajo, que sustancialmente lo mejoraron. También le agradezco el buen ánimo que a todos nos contagiaba, en especial en aquellos momentos cuando las cosas no salían como esperabamos; pero más que nada aprecio mucho su amistad.

To the entire Cardiff team, to Simon Doyle for opening the doors of his laboratory, for his hospitality and all the facilities he provided. To Tom Brien for the good vibes with which he impregnated his presence to the laboratory. To Thomas Gascard for his friendship and trust.

Al equipo de GTM, Diana, Leti, Paola y todos aquellos que me apoyaron y siempre procu-raron que la estadía en Cardiff fuera lo más amena posible, muchísimas gracias a todos ellos, son un gran equipo.

No tendría suficiente espacio para terminar de agradecer a todas aquellas personas y amigos que de forma directa o indirecta han contribuido a éste trabajo, a todos ellos muchísimas gracias, éste trabajo es de todos ustedes.

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This camera belongs to the new generation of instruments to be installed in the Large Millimeter Telescope (LMT). The LMT is the largest millimetre telescope in the world, with a 50 m primary reflector. It is located on the top of the extinct volcano Sierra Negra at 4600 m high in the Mexican state of Puebla. In the 1.1 mm band it is capable of reaching an angular resolution of up to 5.5".

The development of KID detectors goes through a cyclical process of design, manufacturing, readout and characterization of their parameters. The final part of this cycle allows evaluating the performance of the detector according to the needs of the application, to suggest improve-ments in the design and repeat the process consequently. In this sense, because the trend in the development of the instruments points to the exponential increase in the number of detec-tors, as is the case of MUSCAT, the rapid and efficient characterization of all of them becomes essential, to accelerate the consolidation of the final detector design.

In this thesis, I preset a characterization system that includes the readout and quantitative-qualitative analysis of the response of the detectors array as a function of detector base tem-perature, incident optical power, and RF readout power. The readout system, called KID Lab/mux-channel, through the frequency multiplexing technique performs 1) the simultaneous acquisition of the RF transmissionS21 of the detectors for a given span and step size, where it

accurately locates the resonance frequencies and on which the set of readout tones is adjusted to 2) initiate the parallel acquisition of the response of the detectors. From this information, the analysis tool, called KID Analyzer, extracts the physical parameters of the array and its de-tectors such as their resonance frequencies, quality factors, generation-recombination noise level (GR), the quasi-particles lifetime, responsivity, noise equivalent power (NEP), among others.

Applying the above tools, I characterised the distribution and cross-talking between the 243 detectors of one of the full-size prototype array for MUSCAT, where it was observed that the individual response of most of the detectors is appropriate. However, the scatter in frequencies, due to non-uniformity of fabrication processes, reduces the overall yield down to about 80%. Also, in collaboration with the homodyne system of the KID detectors laboratory of Cardiff University, a test array with only 20 pixels were analyzed to evaluate the individual response of the detector, whose results on its noise characteristics indicate suitability for the application.

With the system exposed in this thesis, we seek to promote in Mexico the technological development of millimetric instrumentation based on KID detection, which allows soon to provide instruments of international competence to the LMT, designed and manufactured at INAOE.

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Resumen

MUSCAT es una cámara milimétrica de continuo para la banda de 1.1 mm. Esta formada por seis arreglos de 243 detectores de inductancia cinética (KID) cada uno, para un total de 1458 detectores. Opera a una temperatura de 150 mK, utilizando un innovador sistema de enfriamiento de ciclo cerrado.

Esta cámara pertenece a la nueva generación de instrumentos a instalarse en el Gran Tele-scopio Milimétrico (GTM). El GTM es el teleTele-scopio milimétrico más grande del mundo, con un reflector primario de 50 m. Se localiza en la cima del volcan extinto Sierra Negra a 4600 m de altura en el estado mexicano de Puebla. En la banda de 1.1 mm es capaz de alcanzar una resolución angular de hasta 5.5".

El desarrollo de detectores KID pasa a través de un proceso cíclico de diseño, fabricación, lectura y caracterización de sus parámetros. Este último permite evaluar el desempeño del detector según las necesidades de la aplicación, para consecuentemente sugerir mejoras en el diseño y repetir nuevamente el proceso. En este sentido, debido a que la tendencia en el desarrollo de instrumentos apunta al incremento exponencial en el número de detectores, como es el caso de MUSCAT, se vuelve fundamental la rápida y eficiente caracterización de todos ellos, para accelerar la consolidación del arreglo y sus detectores.

Para ello, en este tesis se ha desarrollado un sistema de caracterización que comprende la lectura y análisis cuantitativo-cualitativo de la respuesta de los detectores del arreglo en función la temperatura base del detector, la potencia óptica incidente y la potencia de lectura. El sistema de lectura, llamado KID Lab/mux-channel, a través de la técnica de multiplexado en frecuencia realiza 1) la adquisición simultánea de la transmisión S21 de los detectores para

un ancho de banda y paso de barrido definidos, donde localiza con exactitud las frecuencias de resonancia y sobre las que ajusta el conjunto de tonos para 2)iniciar la adquisición paralela de la respuesta de los detectores. A partir de esta información, la herramienta de análisis, bautizada como KID Analyser, extrae los parámetros físicos del arreglo y sus detectores como sus frecuencias de resonancia, factores de calidad, nivel de ruido generación-recombinación (GR), tiempo de vida de las cuasi-partículas, responsividad, potencia de ruido equivalente (NEP), entre otros.

Aplicando las herramientas anteriores, se caracterizó la distribución e interacción mutua entre los 243 detectores de uno de los arreglos completos prototipo para MUSCAT, donde se observó que la respuesta individual de la gran mayoría de los detectores es adecuada. Sin em-bargo, la dispersión de las frecuencias, debido a la no uniformidad de los procesos de fabricación, reduce el rendimiento hasta cerca del 80%. Además, en colaboración con el sistema homodino del laboratorio de detectores KID de la Universidad de Cardiff, se analizó un arreglo de prueba con sólo 20 píxeles para evaluar la respuesta individual del detector, cuyos resultados sobre sus características de ruido indican idoneidad para la aplicación.

Con el sistema expuesto en esta tesis, buscamos impulsar en México el desarrollo tecnológico de la instrumentación milimétrica basada en la detección KID, lo que permita en un futuro próximo proveer de instrumentos de competencia internacional al GTM, diseñados y fabricados en el INAOE.

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Chapter 1

Introduction and background

The technological development initiated at the beginning of the last century and exacerbated in the last decades has had a positive impact on practically all the wavelengths that astrophysics uses for the study of the Universe. From the high energies with projects such as the ground-based observatory HAWC (High-Altitude Water Cherenkov Gamma-Ray Observatory) in Puebla or the space observatory GLAST (Fermi Gamma-Ray Space Telescope), to the very low with telescopes such as the 100 m Green Bank Telescope in West Virginia, passing through the recent generation of giant optical telescopes, such as the 10 m GTC (Gran Telescopio de Canarias) in the Canary Islands or the future EELT (European Extremely Large Telescope) of 30 m in Atacama Chile.

In particular, in the millimetre band, the technological momentum reached great notoriety, because its observation offers a unique opportunity for the exploration of the coldest, densest and most-obscured environments of the Universe: early stages of star formation, extra-solar protoplanetary discs, high-redshift dusty starburst galaxies, among others[4]. The construction of the Large Millimetre Telescope LMT at 4600 m in Sierra Negra Mexico, with a single dish recently extended to 50 m and the largest interferometer in the world, the Atacama Large Millimetre Array ALMA in Chile, show its importance.

However, the conflictive nature of this band as a consequence of its location in the electro-magnetic spectrum implies facing great challenges for its detection. Its frequency of operation, the upper edge of the radio, exceeds the capabilities of analogic/digital electronics1_{, in addition}

due to the dimensions of the wavelength of the radiation, the tolerances in the manufacture of electronic systems must be minimal, since even the wires that connect the components can behave like antennas and radiate or receive radiation. On the other hand, it is below the far infrared (FIR) band, where the low energy photons can not promote electrons over the band gap in traditional semiconductor photodetectors, for direct detection, only advanced bolometers (thermal) or superconductor detectors (lower band gap energy), as we will explain later.

Also, the atmospheric opacities become appreciable, both attenuating the sky signal and adding thermal noise to the antenna temperature and as if that were not enough, the receivers are much noisier than those in low-frequency band, forcing them to drastically reduce their temperature in order to detect properly extraterrestrial sources.

1

The analog RF mixers and amplifiers have difficulties up at > 100 GHz. In the practice, they mix the signal down to an IF(intermediate frequency) band and the width of the band is limited by the digital electronics.

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It is only with the development of cooling systems in the order of mK, the elaboration of filters and optical elements with meta-materials[42], very low noise electronic devices operating at higher frequencies, the improvement of frequency reduction (heterodyne) systems and the en-hancement of nanometric manufacturing techniques, which has made possible the strengthening of novel techniques of detection Transition Edge Sensor (TES)[33] and the up-and-coming de-velopment of Kinetic Inductance Detectors (KID) technology [19] for the detection of millimetre radiation.

The mm astronomy community continually demands instruments with higher resolution, spatial or spectral, with the ability to detect increasingly distant and weak sources, with the highest signal-to-noise and in the shortest possible time (integration time). In practical terms, it translates into instruments with more detectors photon-noise limited. In this sense, KID technology has gained considerable visibility for the intrinsic ability to couple a large number of detectors on a pair of transmission lines.

In particular, for the characterization of the increasing number of KID detectors, the need arises to develop readout systems that reliably and quickly acquire the RF transmission-time response of the sensors and, with an analysis system, get its physical parameters. During the detector design stage, characterization plays a critical role for feedback and refinement of its properties, so the reduction in acquisition time and analysis of as many detectors as possible constitutes one of the biggest challenges of the area, and that is the main subject of this thesis.

In this context appears MUSCAT (Mexican-UK Sub-millimeter Camera for Astronomy)[13], a next-generation continuum camera, following to be installed in the LMT, which will oper-ate in the atmospheric window of 1.1 mm. With its continuous closed-cycle cooling system and 1458 KID detectors, it intends to replace the functions of the AzTEC instrument[54], which was the continuum camera used for the first scientific light of the LMT on this 1.1 mm band. The instrument offers the appropriate object of study for the development of the integral characterization system of this thesis, acquiring expeditiously the information of its detectors, through the readout system, to extract the physical properties that allow to evaluate its per-formance and offer alternatives of improvement. Moreover, in order to facilitate and streamline the optimization process of the MUSCAT detectors, I created an application that from the measurements to different conditions of temperature and power supply, obtained with the pre-vious readout system, characterizes the behaviour of the detectors, allowing us to speed up the design-validation-fabrication-characterization process.

Thus, in the whole thesis work, I took advantage of the experience of the characterization experiments and applied it to the development of a readout system divided into six channels for the MUSCAT detectors. Details are presented of the design, constitution and construction of each of the six channels as well as the control software developed, which controls and organizes the frequency sweep process to measure the incident radiation on the KID detectors.

Both applications have their origins in the readout and characterization the MUSCAT de-tectors. However, given the generic nature of the implementation, the systems constitute a very useful tool for the readout and characterization of millimetre KID detectors, whose purpose is to evaluate the design of resonators with different morphologies, materials and manufacturing techniques, for any application, whether or not astronomical.

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1.1 Scientific Motivation

Since MUSCAT will take advantage of the 50 m extension of the LMT single-dish, the largest in the world, with the consequent increase in angular resolution, we have an excellent opportunity for scientific exploration to improve our understanding of the millimetre Universe.

MUSCAT will enable us to expand our knowledge of galactic evolution, to map out star forming regions beyond the Gould belt, and to further investigate the relationship between the evolution of filament structures and star formation processes in our local galaxy[13].

In October 2010 the Herschel-ATLAS survey made public their first 4x4 degree tile, that reached a 5σ noise level of 33.5 mJy at 250 µm [45]. It is the first result of the largest ex-tragalactic survey with Herschel Space Observatory (HSO). It used both the PACS[43] and SPIRE[29] cameras which took pictures in infra-red and submillimetre light at wavelengths of 100, 160, 250, 350, and 500 µm. These maps show a total of approximately 400,000 galaxies with red-shifts ofz= 6, that is, galaxies from the early Universe, when it was less than a billion years old[17].

Nevertheless, due to the limits in the resolution of their instruments, two-thirds of the sources of this catalogue do not have optical counterparts assigned[24]. MUSCAT on the LMT with a resolution of_∼5.5”will help to assign the optical counterparts for the missing sources. From the technological perspective, the development of each one of the stages of MUSCAT involves a titanic task, since each one of them has a complexity for which there is a whole area of scientific and technological development.

Concerning detection, although the use of KIDs has been popularized by the ability to be read in large numbers through a pair of transmission lines, it is also a very young technology in comparison with semiconductors or superconductors bolometers. In this sense MUSCAT is also a pioneering instrument in this detection technology, being the first of its kind to be installed in the LMT and one of the few on-sky as MUSIC[37], ARCHONS[39], NIKA-NIKA2[41][46] and soon BLAST-TNG[23], which is preparing to be launched from the antarctic. In this way, the results and elements contributed by the experience obtained during the development of MUSCAT detectors will be beneficial for the construction of future generations of KID instruments.

The improvement of lithographic techniques at nanometric scales has allowed the manu-facture of KID detector arrays with more and more elements, which represents a significant challenge for the associated readout electronics systems. Although a single MUSCAT channel is capable of readout a large number of resonators simultaneously, to readout arrays of 10,000 pixels, for example, it would take at least ten of them. The problem with this situation is that the current cost per channel is very high, and adding ten or more could make the instrument unaffordable, just for the readout part. The challenge is to significantly reduce the cost and ex-tend the number of detectors per channel. Despite this, it is worth to emphasize that compared with the TES or other systems, the complexity of the cryogenic electronics system is practically null; therefore the costs and development time requirements are considerably lower.

1.2 Millimetre astronomy

The study of the millimetre range began in the sixties with the development of the first receivers with enough sensitivity for the detection of millimetre space sources.

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IR, restricting observation to a small number of atmospheric windows (see Figure 1-1). Even with the best atmospheric conditions (1 to 3 months per year) in the best places on Earth, between 30-40% of the signal is attenuated within the windows 350-450 µm [9]. Any kind of mm radiation outside these atmospheric windows is beyond the reach of any mm ground-based observatory. The only option is to install stratospheric or space-ground-based observatories, such as SOFIA or the HSO, whose only limitation is its low resolution, since at the moment it is impossible to install large telescopes in space.

Under these adverse circumstances, detection technologies were not possible until the end of the last century, when a noise level below the fundamental level of the telescope was achieved, i. e., it reached the photon noise limit, and the quantum efficiency became high enough to take advantage of the little mm radiation collected or the telescopes with large collector areas made their appearance (LMT, IRAM).

The continuum millimetric cameras for the detection of sources used semiconductor bolome-ters, later with the development of novel cooling systems at temperatures below the critical temperature (Tc) of certain bilayers superconductors, such as Ti:Al, Nb:Al and Mb:Cu, was

possible the development of the Transition Edge Sensors (TES) technology. Eventually, the increase in the number of detectors made clear the need to develop more robust readout sys-tems with greater pixel coverage, giving rise to the KID detection technology (mainly using Aluminium Al and Titanium Nitride TiN). Currently, these techniques, TES and KID, dispute the supremacy of the millimetric detection, although there are some efforts to reconcile them by sharing their qualities, as is the case of theµMUX systems[6].

1.3 Millimetre Detectors Background

In this section we will briefly analyze the status of low noise sensors for the development of continuum cameras, TES and KID, comparing them, analyzing their readout systems and exposing the challenges they face in particular.

1.3.1 Transition Edge Sensors TES

When the temperature of a superconductive material falls below the threshold ofTc its crystal

lattice changes in such a way that its free electrons group in pairs forming Cooper pairs. The crystal distortions move through the material carrying the electron pairs with them. If an electric field is applied, they can move freely without dissipative mechanisms, that is, the electrical resistance of the material vanishes. This behaviour occurs in the transition region just below Tc, where the change in electrical resistance in relation to the temperature change

is abrupt[2].

A TES bolometer (Figure 1-2a) is a highly sensitive thermometer composed of a ducting thin film weakly heat-sunk to a bath at a much lower temperature than the supercon-ductingTc[6]. It operates just in the superconducting-to-normal transition, in such a way that

small changes of temperature, as a result of the radiation incident in the detector, lead to large changes in their electrical resistance (Figure 1-2b).

In superconductive detectors, as TES, the power dissipation V2/R opposes the changes in the incident power. This is known as negative electrothermal feedback, keeps the detector at a relatively constant temperature. A further explanation can be found in [2]. This feedback

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Cryogenic subsystem

The cooling subsystem of MUSCAT is divided into three subsystems: a Pulse Tube Cooler (PTC)5_{, two continuous sorption (CS) coolers} 6 _{and a miniature dilution (MD)}7 _{refrigerator.}

The pulse tube cooler is in charge of the cooling of the first two stages of the cryostat: the 50 K stage, used as heat sinking point; and the 4 K stage, which contains the readout amplifiers, and is used as a thermal bath for both continuous sorption coolers.

The continuous sorption coolers are responsible for the following two stages: the 1 K stage, which provides heat sinking for readout and the 350 mK stage, that is part of the condensing point for the MD fridge.

At last, the MD moving helium-3 molecules across the phase boundary between helium-3 rich phase and helium-3 poor phase, reaching 70 mK in the initial dark unloaded configuration and settles at 150 mK in the optically open fully loaded system. Which is ideal for the aluminium LEKIDs.

Detectors

The detection stage of MUSCAT consists of six multiplexed arrays with 243 aluminium horn-coupled LEKID deposited on three silicon wafers (two arrays per wafer).

Figure 1-11a shows the final design of one of the MUSCAT detectors. The shape of the meander of the detector, which makes up the detection region, is such that the horizontal sections are approximately the same length as the vertical sections, this gives sensitivity in both types of polarization. Although it is not able to discern the type of polarization of radiation, it is capable of detecting twice as much radiation as those that do detect the type of polarization. There are other proven configurations capable of detecting both polarizations, as in the case of the Hilbert pattern structure Figure 1-11b. The meander section was designed to absorb equally in both orthogonal polarisations and simulations of the entire meander + silicon wafer + quartz AR coating + free space air gap + feedhorn/waveguide/choke system were optimised in HFSS to maximise optical absorption efficiency and minimise stray light leakage.

The resonance frequency of each detector can be adjusted by changing the length and number of fingers of the interdigital capacitor. In MUSCAT, the resonance frequencies of the arrays occupy the 500 MHz - 1 GHz band, with an average distance between detectors of _∼2 MHz. The coupling quality factors are designed to be 50000 and this is tuned as a function of design resonance frequency by adjusting the length of additional capacitor to ground.

Each of the arrays is divided into two bands, low-frequency groups a total of 135 detectors between 500-750 MHz and high frequency from 750 MHz to 1 GHz with 108 detectors. The frequency spacing is designed to increase linearly with frequency. The quality factor and the spacing in linewidths was also chosen to be constant, so the spacing in frequency has to increase linearly with frequency.

5

Cryomech Inc. Model PT-420-RM.

6

Chase Research Cryogenics Ltd CRC.

7

ibid.

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• As part of its main objectives of the MUSCAT project is the technology transfer from the United Kingdom to Mexico. In this way, LEKID detectors have already been designed by Victor Gómez, and manufactured in INAOE laboratories by Abel Perez, with arrays of 20 resonators of the same quality as those manufactured in Cardiff. Regarding the readout system, this thesis is partly a testament to that, with the readout system and the KID detector characterization tool, products of this work, it is intended in the coming months to make the first frequency multiplexed readout of KID millimetre detectors in Mexico, opening a window of opportunity for the development of KID technology for upcoming instruments in the LMT.

• The possibility for the LMT and INAOE to be part of international consortiums devel-oping and leading instruments.

1.6 Objectives

The main objective of this thesis is to develop an integrated system for the rapid and adequate characterization of KID millimetre detectors, capable of simultaneously acquiring the response of all detectors coupled to a single transmission line, and quantifying their physical properties to assess their quality and performance. The context under which we propose this system requires that both the hardware and part of the system software tools be designed and constructed according to the MUSCAT requirements.

It contemplates the fulfilment of the following particular objectives:

1. To assemble and launch the hardware of the six MUSCAT readout channels. Integrate the channels with the rest of the elements of the readout system to the MUSCAT readout rack.

2. To develop the readout control system for the MUSCAT channels based on frequency multiplexing technique. Extract the transmission or S21 parameter from the resonators

of one of the MUSCAT arrays through a frequency sweep, as well as the time streams of the readout tones at the array resonance frequencies.

3. To develop a characterization system for kinetic inductance detectors. From the data generated by the readout tool, characterize the response of the detectors to know their physical characteristics such as resonance frequency, quality factorsQr,Qc,Qi, the

nonlin-earity parameter; Two-Level System (TLS), generation-recombination and amplifier noise levels; the quasi-particles lifetime, as well as their responsivity and the noise equivalent power(NEP).

4. With the physical parameters of the previous point, evaluate the performance of the MUSCAT detectors, such as the set of resonators coupled to the same feedline that interact with each other (detectors array) and as individual elements.

1.7 Thesis Outline

The outline of this thesis follows:

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• Chapter 2introduces the physics of superconducting detectors KID, as well as the read-out system of frequency multiplexing. Particular emphasis is placed on those features of the detector to optimize the detector readout.

• Chapter 3 describes the construction process of the six MUSCAT channels and the

integration of the readout system into the readout rack.

• Chapter 4presents the development of the readout control system, based on the existing

kidPy firmware and software library, and the newly developed PCP software library, which operates the readout channel of Chapter 3 in order to sweep detector arrays and get its time stream.

• Chapter 5 describes the detectors characterization system that, based on the measure-ments obtained by the readout control system, obtains those parameters that allow eval-uating the quality of the detectors.

• To validate the operation of the tools developed in this thesis; in the first part of Chapter 6 we present the readout results of one of the large MUSCAT array using the readout system of Chapters 3 and 4 as well as the characterization as detectors array through the tool of Chapter 5. In the second part, we show the results of more in-depth detectors characterization, reading out one of the small MUSCAT arrays through the homodyne system of the KIDs laboratory of Cardiff University, and again analyzing them with the application of Chapter 5.

• Finally in Chapter 7, I conclude the thesis and present the future work for further

improvements based on this work.

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Chapter 2

Physics of the superconducting

detectors and the readout system

In this chapter I present the physical fundamentals that explain the resonance frequency changes in a KID superconducting detector, depending on the amount of radiation absorbed.

It begins with a brief introduction to the superconductivity that takes place in certain ma-terials when they reach temperatures belowTc, analyzing the qualities of perfect conductivity

and diamagnetism through the classic London model, and how they change according to the type of current applied: AC or DC. Also, in a basic but sufficient way, I introduce the quantum model of the Bardeen-Cooper-Schrieffer (BCS) theory, which describes more precisely the su-perconductive state, starting from the grouping of electrons in Cooper Pairs with an energy gap

∆associated. Given the practical objective of the thesis, the theory presented here highlights those results and predictions that have direct application in the design and readout of KID detectors.

Continues with the description of the operation of the KID detector, leading the classical model of a resonator circuit to the field of superconductivity. I expose its main characteristics and how they contribute to the intrinsic noise of the resonator depending on the conditions of power supply and operating temperature.

Having understood the character of the KID detectors and the set of parameters involved, I introduce the frequency multiplexing readout system that will allow us to readout a large number of detectors coupled to the same transmission line. Finally, I expose each of the stages that comprise it together with a brief description of the hardware and software used.

2.1 Principles of superconductivity

In 1911 at the University of Leiden, the Dutch physicist Kammerlingh Onnes, after several years of work perfecting the cooling techniques to reach temperatures of a few Kelvin, observed that in some metals such as mercury, lead and tin, the electrical resistance disappeared completely when the temperature dropped below a critical temperature Tc characteristic of each material.

Prior to his discovery, which earned him the Nobel Prize in Physics in 1913, it was thought that because the electrical resistance of metals is related to the thermal movement of the particles, if we reduce the temperature we would expect the resistance reduce as well, so even at very low

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h=−c _{∇ ×}(ΛJs), (2-4)

whereJscorresponds to the supercurrent density andΛ is a phenomenological parameter given

by

Λ = 4πλ

2

c2 =

m nse2

. (2-5)

e: The electric charge of the electron ∼ −1.6×10−19 C. m: The mass of the electron _∼9.1_×10−31 kg.

ns: The density of superconducting electrons. It varies continuously from zero, at temperatures

aboveTc, up to a limit valuen, corresponding to the density of conductive electrons atT << Tc.

The first of equations (2-3) describes the perfect conductivity. It proves that the electric field accelerates superconductive electrons instead of keeping them at a constant speed due to the opposition of the electrical resistance of the material, as in the non-superconductive regime. This dissipative nature is described by the standard Drude model for electrical conductivity, which, from the classical perspective of Newtonian mechanics, defines the movement of electrons as:

m dv/dt=eE₋mv/τ. (2-6)

v: The average drift velocity of electrons.

τ: The phenomenological relaxation time, which describes the time it would take for an electron

to disperse along the material, by contact with other particles, reducing its velocity fromv to zero.

Equation 2-6 indicates that the average velocity of free electrons is the product of two opposing forces, on the one hand, the electric field accelerates the electrons, and on the other, the collisions with other particles of the material structure change their direction and reduce their movement. They only reach an equilibrium state when the electron velocity is constant and equal to v = eEτ /m. Hence, the movement of n electrons per unit volume moving at a drift velocityv, causes an electric current density of the form

J =nev =n(e2τ /m)E=σE, (2-7)

which leads to the classical expression of Ohm’s law. It is concluded, then, that the conductivity

σ, typical of each material, depends directly on the efficiency in the dispersion of electrons. It would explain why decreasing the temperature of a normal material also decreases its resistance, since the reduction of collisions between particles accompanies the reduction of the movement of electrons. However, it does not justify the behaviour seen in superconducting materials, where passing the temperature thresholdTc, there is an absolute absence of resistance.

This would imply the existence of a density of superconducting particlesns, whose electrons,

under the absence of collision dispersion, would move indefinitely, that is, the relaxation time of these superconducting particles τs would tend to infinity. Therefore, adjusting equation 2-6,

we have

dvs/dt=eE/m, (2-8)

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where we enter the superconductive drift velocity term vs. The lack of forces that counteract

the electric field produces the acceleration of the supercurrent Js, which similar to (2-7) we

define as:

dJs/dt= (nse2/m)E = (c2/4πλ2) =E/Λ, (2-9)

which is equivalent to the first London equation (2-3).

On the other hand, combining Maxwell’s equations that describe the laws of induction of Faraday and Ampere:

∇ ×E=₋1 c

∂h ∂t →

∂h

∂t =−(∇ ×E)c, (2-10)

∇ ×h= 4πJ/c_{→ ∇ ×}∂h ∂t =

4π c

dJ

dt, (2-11)

and applying equation 2-9, we get

∇ ×(−∇ ×E)c= 4π c dJ dt = 4π c2 c2

4πλ2E → −∇ × ∇ ×E =∇ 2

E =E/λ2. (2-12) The solution of differential equation 2-12, reveals that the time-dependent electric fields decay exponentially as they enter the material, until they practically disappear at a distanceλ from the surface.

London’s second equation demonstrates that this behaviour also occurs with the magnetic field in superconducting materials, as described by the Meissner effect. To do this, applying the rotational to both sides of the Maxwell 2-11 equation, we have

∇ ×h= 4π

c J → ∇ ×(∇ ×h) =∇ ×(

4π

c J)→ ∇ ×(∇ ×h) =

4π

c ∇ ×J. (2-13) Substituting the second London equation (2-4) in 2-13

−∇ ×(∇ ×h) = 4π

c2(

c2

4πλ2)h,

− ∇ ×(∇ ×h) = (1/λ2)h_{→ ∇}2h=h/λ2, (2-14) whose solution is of the form

h(x) =h(0)e−x/λ_. _(2-15) x: It is measured from the surface into the material.

λ: Penetration depth, which in terms of 2-5, is

λ2 = mc

2

4πnse2

= m

µ0n_se2

, (2-16)

whereµ0 is the magnetic permeability in vacuum, µ0 = 4π

c2 ∼4π×10−

7_{W b}

Am

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Equation 2-14 clearly shows the exponential reduction of the magnetic field within a su-perconducting material until it runs out at the penetration distanceλ, which depends on the density of superconducting elementsns, intimately linked with the temperature. Experiments

at temperatures well below Tc, of pure samples of superconductors, exhibit λ∼500Å. While

materials with short mean free path, such as dirty superconductors, or short coherence length as high-temperature superconductors, have higher values ofλ, typically higher than1500Å.

2.1.2 The Two fluid model

The previous treatment of superconductivity, through the principle of perfect conductivity or zero resistance, establishes the creation of a lossless electric current using a continuous DC electric field. However, this property is not extensive when we apply a variable AC electric field, where there is energy dissipation.

The reason is due to the finite inertia of superconductive electrons that allow the existence of internal AC electric fields, which originate small populations of normal electrons, so-called as quasi-particles, as would be expected at temperatures above Tc and not below. In not

very strict but straightforward terms, the alternating movement of superconducting electrons produces "heat", which destroys the state of superconduction and promote the creation of these quasi-particles. Its simple presence is responsible for the small nonzero dissipation for AC currents, according to Ohm’s law of equation 2-7.

From this perspective, in 1934 Gorter and Casimir[1] propose the analysis of a supercon-ductor under an AC electric field, such as the superposition of two fluids with different density: one dissipative consisting of quasi-particlesnqp and the other non-dissipative formed by

super-conducting electronsns, grouped in pairs known as Cooper Pairs.

This model estimates that the quasi-particle density is directly proportional to the tempera-ture2 _{of the form}

nqp∼(T /Tc)4 3and in a complementary way, the density of superconducting

particles followsns∼1−(T /Tc)4. The relationship between populations can be written as:

ns/nqp ≈(Tc/T)

4

−1. (2-17)

The total impedance in a superconducting material has a real resistive component due to

the ohmic dissipation of the quasi-particles; and an imaginary component reactive, product of the kinetic inductance, generated by the transformation of the energy of the electric field to kinetic energy of the superconducting particles, plus the contribution by the inertia of quasi-particles. Due to the dependence of the impedance with the frequency of the AC electric field that feeds the movement of particles, we analyze two extreme cases:

• Atlow frequenciesthe quasi-particle populationnqp decays and the conductivity by

super-conducting electrons is dominantσs>> σqp. The extreme case occurs when the frequency

is zero, the electric field becomes DC, causing the disappearance of the quasi-particles to-gether with the electrical resistance of the material. Besides, since the reactance is directly proportional to the frequency, XL =ωL, under these circumstances, its contribution to

2

Temperature belowTc, 0≤T < Tc

3

A more accurate approximation is offered by the BCS theory,nqp∼e−∆/KT, which saves the behavior oft4

but falls exponentially to zero at low temperatures, as is not the case with the Gorter-Casimir power law

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2.1.3 The internal inductance of a superconductor

In the previous section, we can see that superconductive electrons under an alternating current have inductive properties. This internal inductance L can be expressed in terms of two main components

L=Lk+Lm. (2-19)

Lk: Kinetic inductance related to the kinetic energy of superconducting electrons.

Lm: Magnetic inductance. Coming from the magnetic field energy created by Js and stored

within the volume of the superconductor.

It is possible to calculate the kinetic inductance from the kinetic energy that contributes to the supercurrent densityJs. Thus, the kinetic energy K per unit volume is

K= 1 2nsmv

2

s, (2-20)

wherevs is the speed of superconducting electrons. By adjusting equation 2-7, we can calculate

the current density Js in terms of the velocityvs as

Js=−nsevs. (2-21)

Combining 2-20 with 2-21 and using the definition of the penetration depth of equation 2-16, we have

K = 1

2

m nse2

J_s2 = 1

2µ0λ

2

J_s2. (2-22)

We can express 2-22 in terms of energy per unit of length KL by integrating the entire

cross-section of areasas follows

KL= 1₂µ0λ2 Z

s

J_s2ds. (2-23)

Moreover, the classic formula to express the energy stored in the form of a magnetic field in an inductorLk through which a currentI circulates is

E= 1

2LkI

2

. (2-24)

Finally, by equating equations 2-23 and 2-24 we find the general formula of kinetic induc-tance as

LkI2=µ0λ2 Z

s

J_s2ds_→Lk=

µ0λ2

I2 Z

s

J_s2ds. (2-25)

In the case of a material whose current distribution is uniform throughout the cross-section, the kinetic inductance is reduced to Lk = µ0λ2. However, this simplification does not apply

to superconductors, because the non-homogenously current is confined to a region that starts from the surface and to depthλas London model suggests.

Simon Doyle [21] proposes a general solution to equation 2-25 along with an expression for the magnetic inductance Lm

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Figure 2-4: The ratio of the components of magneticLm(red) and kineticLk(black) inductance,

of the total internal inductance of the resonator, as a function of the film thickness for the Aluminium. As we reduce the thickness, the kinetic inductance becomes predominant. Image taken from [21].

Lk=

µ0λ

4W coth _t 2λ + _t 2λ csc2 _t 2λ , (2-26)

Lm=

µ0λ

4W coth _t 2λ − _t 2λ csc2 _t 2λ , (2-27)

t: The height of the cross section of the superconductor. W: The width of the cross-section.

Then, substituting 2-26 and 2-27 in equation 2-19, we obtain the total internal inductance in terms of the thickness of the filmt and the wavelengthλ:

L=Lm+Lk =

µ0λ

2 coth

_t

2λ

. (2-28)

The contribution of the kinetic inductanceLk and magneticLm to the total internal

induc-tance, according to equations 2-26 and 2-27, depends on the thickness of the filmt, as illustrated in Figure 2-4. In a thick film, whose thicknesstis much larger thanλthe contribution of both inductances tends to be similar. On the contrary, in a thin film, which thickness is much less thanλ, the contributionLk is dominant, and in some cases absolute.

In KID detectors, whose operating principle is based on the disturbance of the kinetic inductance, the higher the contribution of Lk toL, the higher its sensitivity. In terms of the

thickness of the superconductor film,the thinner it is, the greater the sensitivity of the detector.

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unloaded Q, denoted as Qi.

Regarding the input impedance of the RLC resonator circuit of Figure 2-6, this is

Zin =

1

R +

1

jωL+jωC

−1

, (2-34)

and the complex power delivered on the resonator is

Pin =

1 2V I∗=

1 2|V|

2 1

Zin =

1 2|V|

21

R + j

ωL−jωC

. (2-35)

On the other hand, the power dissipated by the resistance is

Ploss= 1₂|

V_|2

R . (2-36)

We can rewrite the input impedance in terms of the stored energy We,Wm and the power

dissipated as:

Zin = 2Pin

|I_|2 =

Ploss+ 2jω(Wm−We)

1 2|I|

2 . (2-37)

In resonance, whereWe=Wm, and according to 2-36, equation 2-37 is reduced to

Zin =

Ploss

1 2|I|

2 =R, (2-38)

the impedance is completely real.

Analyzing the input impedance of equation 2-34 in the region near the resonance ∆ω, so thatω =ω0+ ∆ω, we rewrite 2-34 using the series expansion as

Zin≃

1

R +

1−∆ω/ω0

jω0L +

jω0C+j∆ωC −1

≃ _{1 + 2}_jR_∆_ωRC = R 1 + 2jQi∆ω/ω0

. (2-39)

By definition the half-power fractional bandwidth of the resonator has its limits on frequen-cies such that the average power delivered to the circuit is one-half that delivered at resonance, that is when the frequency is such that _|Zin|2 = R

2

2 . If BW is the fractional bandwidth, then

∆ω/ω0=BW/2. Applying this condition to 2-39, it turns out:

BW = 1 Qi

. (2-40)

Equation 2-40 has important implications in the design and readout of KID resonators. If we want to place as many resonators as possible on a given bandwidth without overlapping, the quality factor has to be as high as possible. As we saw, the Q value depends on the dissipation of energy, that is, on the equivalent resistance R, which in the design must be reduced as much as possible to increase Q. In the superconductive resonators, minimum values of non-zero resistance can be achieved, due to to the alternating current with which they feed.

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is the fractional detuning of the readout generator frequencyωg relative to the resonance

fre-quencyω0. Function 2-43 has the typical Lorentzian curve centered aroundω0, with half-width

bandwidth ωr/2Qr [9].

Varyingx, sweeping the generator frequency draws a circle in the complex planeS21. At the

resonance frequency, ωg=ω0,x= 0and the circle crosses the real axis at the closest approach

to the origin [51].

2.2.3 Power Dependence

The strength of the signal of the detectors readout affects the resonator response of equation 2-43. As it increases, non-linear behaviour is revealed in their response. The most relevant source on nonlinearity comes from the current dependent non-linear kinetic inductance of the superconducting film [51].

The non-linear kinetic inductance brings with it the resonance frequency shift δω0. Hence

the resonance frequency of the non-linear resonator isωn,0=ω_l,0+δω0, where whereω_l,0 is the

low-power resonance frequency [51]. We rewrite 2-44 as

x= ωg−ωl,0−δω0

ωl,0−δω_r ≈

x0−δx, (2-45)

where the first-order approximation is made, so that

x0=

ωg−ωl,0

ωl,0

, (2-46)

equivalent to detuning in the linear limit of 2-44. While the non-linear frequency shiftδx=−EE∗, where the scaling energy isE_∗αLkI_∗2/α2 [51].

On the other hand, following the analysis of [9] the power dissipated in the resonator can be expressed by conserving the power of a signal trough the feedline such as:

Pdiss

Pg

= 1_{− |}S21| 2

− |S11| 2

(2-47)

For a shunt-coupled circuit S11=S21−1, and substituting 2-43 in 2-47, it turns out

Pdiss

Pg =

"

2Q2

r

QiQc

1 1 + 4Q2

rx2

#

. (2-48)

The terms on the right are known as the coupling efficiencyχc and the detuning efficiency

χg. Both have a maximum value of one unit, χc reaches the maximum whenQi=Qc while χg

is maximum at the resonance frequency.

Also, by summarizing the resonator’s total energy as E = We+Wm, we can rewrite the

definition of the quality factor of 2-33 as

Qi =ω0

E Pdiss

, (2-49)

we calculate the total energy of the resonator in terms of the power feeding and the factors of quality like

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Figure 2-9: Resonator response in overdriven according to the sweeping direction. In the upwards frequency sweeping (above) as the sweep tone approaches the resonator, its resonance frequency approaches, so that we quickly map the response of the resonator (positive feedback). While in the downwards frequency sweeping (below) the resonance frequency moves away from the tone, so that the resonator mapping is slower. Graph taken from [51].

The response in the bifurcation state depends on the sweeping direction: a) upwards fre-quency, as the tone approaches the resonance, the power supply reduces the resonance frequency approaching the tone, in a positive feedback process, so that we quickly traverse the response of the resonator, according to the upper graph in Figure 2-9. Moreover, b) downwards frequency, whereas the sweep tone approaches the resonance, it moves away, delaying the full resonator sweep (lower graph in Figure 2-9).

2.2.4 Noise parameters

In KID superconducting detectors, there are two fundamental sources of noise: i) Two-Level System (TLS) noise at low frequencies, ii) Generation-Recombination (GR) noise. In practice to these sources, the noise of the low noise amplifier placed at the output of the resonator must be added.

TLS Noise

In practice, an excessive amount of noise has been observed in the resonance frequency, which varies according to _∼ f−12. It is derived from the effect of Two-Level Systems (TLS), which is basically due to fluctuations of the complex dielectric constant of the material, due to the morphic structures of the dielectric materials.

Some experiments have demonstrated that TLS noise is wholly associated with the resonator capacitor, not the inductor, which leads to the change in its resonance frequency.

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Gao 2008 [26] derives an expression of the spectral density that brings the TLS noise to the resonance frequency fluctuations of the detector. The specific form depends on the geometry and the material, but can be expressed as the scaling relation, according to Barry 2014 [9]

ST LS∝T−βPg−1/2, (2-55)

where T is the temperature of the superconducting material andβ is between 1.5 and 2 [56]. There are several ways to reduce TLS noise from the detector design, exploring with dif-ferent capacitor geometries, using titanium nitride that does not develop a natural oxide by reducing the disturbances of the complex dielectric constant or removing any active oxide before depositing the superconducting film.

It has also been observed that the increase of the detector readout power reduces the in-tensity of the TLS noise, due to its saturation. It represents the leitmotiv of this thesis and plays a crucial point in the readout of KID detectors, wherewe seek to increase as much as possible the readout power to reduce TLS noise, but enough to avoid inducing the overdriven state in the resonator.

GR Noise

In a superconducting material in thermal equilibrium, the density of quasiparticlesnqp per unit

volume is [20]

nqp= 2N0

√

2πkT∆exp(−∆/kT), (2-56) when kT < ∆, where N0 is the single spin density of states at the Fermi level (1.72 ×

101₀

µm−3_eV−1 for Al) and _k is Boltzmann’s constant. Assuming the thermal distribution of quasi-particles and phonons, the average quasi-particle lifetime (the time it takes to recombine the quasi-particles in Cooper pairs) is given by [21]

τqp =

τ0

√_π kT_2∆c

5_/2! s

Tc

T exp(∆/kT) = τ0

nqp

N0(kT)3

2∆2 , (2-57)

where τ0 is the characteristic interaction time between electron-proton and depends on the

material.

The GR noise that represents the fundamental limit in any KID is due to statistical fluctu-ations in the density of Cooper pairs/quasi-particles within the volume of any superconducting material. Its spectral density, as a Lorentzian spectrum, is given by [53]

SGR(ω) = 4Nqpτqp

1 + (ωτqp)2

, (2-58)

whereω is the spectral angular frequency.

Since this noise is proportional to the number of quasi-particles in the superconducting material, its corresponding NEP is [49]

N EPGR= 2∆

q

Nqp/τqp. (2-59)

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GR noise can be reduced, reducing the number of quasi-particles, the film volume or the material temperature (pairing quasi-particles in Cooper pairs).

2.3 Readout of frequency multiplexing systems

In order to measure the number of millimetre and submillimetre photons responsible for the breaking of Cooper pairs in quasi-particles, which fall on each detector, there are several meth-ods: a) measuring the displacement of the resonance frequency of the sensor, taking advantage that it depends on the intrinsic kinetic inductance of the detector which in turn depends on the number of quasi-particles present, b)measuring the zero-cross phase of the resonator, similar to the previous method, or c) quantifying the change in the quality factor of the resonator by the increase in the dissipation of energy derived from the rise in the quantity of quasi-particles, elements of a dissipative nature.

Whatever the case, for all of them, we need to know the scattering parameter S21, that is,

the transmission of the detector as a function of frequency. It is this peculiar characteristic, the fact that the readout of the resonators happens in the domain of the frequency, the one that allows us to readout thousands of detectors through a simple pair of transmission lines, which it is known as frequency multiplexing. This way of readout represents a significant reduction in costs and the complexity of the system, which explains the recent success of KID detectors and their growing use in astronomical applications, in the millimetre and submillimetre bands in particular.

The fundamental objective of the KID detectors readout system is to generate a set of tones corresponding to the resonance frecuency of each detector of the array. Then varying the frequency of this comb of tones, we "sweep" the response of the sensor in a defined bandwidth to quantify their physical parameters: measuring the displacement of the resonance frequency or the decreasing of the quality factor and estimate the number of incident photons.

As shown in Figure 2-10, the readout of multiplexed frequency systems consists of the following three modules:

1. Readout control system. It executes the readout tasks of the detectors synchronizing all the devices that participate in it: tone generator, synthesizer, attenuators, etc. Initializes the system, defines the list of tones and the criteria for the selection of resonance frequencies, manages the storage of data, among others.

2. Digital tone processor. Generates the digital tones and changes them to analog signals through a Digital-Analog DAC Converter, to be transferred to the multiplexing chan-nel, henceforth mux-channel. Likewise, the output signals of the cryostat that are pre-processed by the aforementioned mux-channel are digitized through an Analog-Digital Converter ADC to finally be processed and transmitted to the control system.

3. Mux-channel. Mixes (modulation) each of the tones with the frequency of a local

oscil-lator controlled by the control system, regulates its power and feeds with it the array of superconducting detectors installed inside the cryostat. The output signal of the detector array follows a similar process, although inverted, after controlling the input power to the channel, the signal is extracted from the local oscillator (demodulation) and sent for analysis back to the tone processing stage.

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tool is designed to work with the ROACH-2 FPGA system. It has real-time monitoring of the input/output signals for power control, looking for the highest signal SNR without saturating the system. It also has the functions of sweeping by the detector and over a full bandwidth (VNA sweep) as well as capturing thetime stream at a specific tone to characterize the sensor. For the development of the readout control system proposed in this thesis, which is described in Chapter 4, part of the essential functions provided by the kidPy library.

2.3.2 Digital tone processor

At this stage, a Digital Signal Processor (DSP) generates a comb of digital probe tones 5 _of

the list provided by the control system. Since it is required that the signal carrying the tones be continuous, it will be necessary to convert the digital signal from the processor to an analog signal through a DAC. Moreover, the output of the detector is digitized employing an ADC, transmitted and processed to the DSP, and finally sent to the control system for storage.

For this kind of application, the sampling frequency of the ADC and DAC must be high enough, at least twice the total bandwidth of the comb of tones (Nyquist criterion), to read the signals thoroughly and reduce aliasing. MUSCAT detectors are designed to operate in an approximate bandwidth of 500 MHz, between _∼500₋1000 MHz. Under this condition, the MKID DAC/ADC Board was selected (see Figure 2-12). It combines two channels of Digi-tal/Analog conversion (Texas Instruments TI DAC5681) with two channels of Analog/Digital conversion (TI ADS54RF63) and a low-noise reference (ADR441) on a single board using ZDOK connectors for any ROACH model. Its main technical characteristics are:

• DAC of 2 channels with SMA connectors. 16-bit resolution and 1 GS/s sampling rate

• ADC of 2 channels with SMA connectors. 12-bit resolution and 550 MS/s sample rate

• Separate clock inputs for ADC and DAC

• It has synchronization input for a PPS signal (one pulse per second).

• Power dissipation of 8.5 W

Apparently, the Nyquist sampling frequency of the ADC, 275MHz, is not sufficient for the bandwidth of the MUSCAT detectors. Nevertheless, we can use both channels of each converter to process the in-phase (I) and quadrature (Q) frequency components of the comb probe, doubling the effective bandwidth at 550MHz, sufficient for a MUSCAT channel.

Regarding the DSP, although it is possible to use any board capable of handling a large amount of data, hundreds or even thousands of Gigabits per second, the ROACH-2 board (Reconfigurable Open Architecture Computing Hardware version 2, see Figure 2-13) developed by CASPER (Collaboration for Astronomy Signal Processing and Electronics Research) has become popular in radio astronomy, because it is all open source with many libraries for com-munications and design of logic, it is easily reprogrammable, and its connectivity/hardware

5

It should be noted that the criteria to create the tone list are proposed and applied by the control system. The digital tone processor merely executes the order, as long as the tones are within the bandwidth allowed by the system; otherwise it just ignores them.

Readout and characterization system for kinetic inductance detectors (KID) of the MUSCAT project.

Readout and characterization

system for kinetic inductance

detectors (KID) of the MUSCAT

project.

by

Marcial Becerril Tapia

Thesis submitted in partial fullfillment of the

requirements for the degree of

MAESTRO EN CIENCIAS en la especialidad de

ASTROF´ISICA

at the

Instituto Nacional de Astrof´ısica, ´

Optica y

Electr´onica

December 2019

Tonantzintla, Puebla

Advised by:

PhD. Abraham Luna Castellanos

Researcher - INAOE

PhD. Edgar Castillo Dom´ınguez

Project Lead - SRON

PhD. Sam Rowe

Research Associate - Cardiff University

c

INAOE 2019

The author hereby grants to INAOE permission to

reproduce and to distribute publicly paper and

electronic copies of this thesis document in whole or

Readout and characterization system for kinetic inductance

detectors (KID) of the MUSCAT project.

Marcial Becerril Tapia

Instituto Nacional de Astrofísica, Óptica y Electrónica

Agradecimientos

Contents

Chapter 1

Introduction and background

1.1

Scientific Motivation

1.2

Millimetre astronomy

1.3

Millimetre Detectors Background

1.6

Objectives

1.7

Thesis Outline

Chapter 2

Physics of the superconducting

detectors and the readout system

2.1

Principles of superconductivity

2.3

Readout of frequency multiplexing systems