Characterization of Transition Edge Sensors for the Millimeter Bolometer Array Camera on the Atacama Cosmology Telescope Yue Zhao A dissertation presented to the faculty of Princeton University in candidacy for the degree of Doctor of Philosophy Recommended for acceptance by the Department of Physics Advisor: Suzanne T. Staggs November 2010 c Copyright by Yue Zhao, 2010. Abstract The Atacama Cosmology Telescope (ACT) aims to measure the Cosmic Microwave Back- ground (CMB) temperature anisotropies on arcminute scales. The ACT project is producing high-resolution millimeter-wave maps of the sky, which can be analyzed to provide measure- ments of the CMB angular power spectrum at large multipoles to augment the extant data to improve estimation of such cosmological parameters as the scalar spectral index and its running, the density of baryons, and the scalar-to-tensor ratio. When combined with X-ray and optical observations, the millimeter-wave maps will help to determine the equation of state of dark energy, probe the neutrino masses, constrain the time of the formation of the first stars, and reveal details of the growth of gravitationally bound structures in the universe. This thesis discusses the characterization of the detectors in the primary receiver for ACT, the Millimeter Bolometer Array Camera (MBAC). The MBAC is comprised of three 32 by 32 transition edge sensor (TES) bolometer arrays, each observing the sky with an independent set of band-defining filters. The MBAC arrays are the largest pop-up detector arrays fielded, and among the largest TES arrays built. Prior to its assembly into an array and installation into the MBAC, a column of 32 bolometers is tested at approximately 0.4 K in a cryostat called the Super Rapid Dip Probe (SRDP). The purpose of this paper is twofold. First, we will describe the SRDP measurements that supply important TES operating properties. Second, we will expand upon the ideal TES bolometer theory to develop an extended thermal architecture to model non-ideal behaviors of the ACT TES bolometers, emphasizing a characterization that accounts for both the complex impedance and the noise as a function of frequency. iii Acknowledgements Everything that has a beginning has an end. This thesis is the culmination of the last four years of my research on ACT TES bolometers. First and foremost, I must thank my grandfather, Professor Hsio-Fu Tuan, who taught me through his own example that despite all the sacrifices and hard work necessary for pursuing a career in science, it is a field of truth and beauty worthy of a lifetime’s devotion. I have always looked up to my grandfather as a pure scholar, and a man of passion who dedicated his life to the science and education of his motherland. It is still my dream to one day become a scientist as great as him. I miss him dearly. I am extremely grateful to have Professor Suzanne Staggs as my research advisor. She has not only guided my work with great insights, but also allowed great flexibility in my research method and schedule. Much of the ACT bolometer research presented in this thesis is a continuation of the earlier efforts of Rolando D¨unner and Tobias Marriage. Norman Jarosik made this research possible by designing and building the data acquisition system, and has continued to provide guidance whenever I have questions about any aspect of my research. I have directly worked with Michael Niemack, John Appel, Omelan Stryzak, Ryan Fisher, Lucas Parker, Thomas Essinger-Hileman and Krista Martocci on testing the TES column assemblies that eventually went into the MBAC. I thank Professor Lyman Page for providing comments on physics research in general. Even though I have not worked with them on TES research directly, I also thank Adam Hincks, Judy Lau, Glen Nixon, Katerina Visnjic and Professor Joe Fowler for making the experimental gravity group at Princeton a truly supportive and productive environment. More broadly, I would also like to thank all the collaborators of the Atacama Cosmology Telescope experiment and the Atacama iv B-mode Search experiment that I became involved with during my last few months at Princeton; it feels great to be part of a scientific community that strives to achieve the best. The NASA Goddard Space Flight Center fabricated the TES detectors that are pre- sented in this thesis. In particular Jay Chervenak provided much guidance on detector characterization. More generally, our detector characterization is based on the seminal works of John Mather, Harvey Moseley, Kent Irwin, Mark Lindeman, Enectal´ıFigueroa- Feliciano and Dan McCammon, although this list is certainly far from exhaustive. Before joining the ACT experiment, I worked with Professor Cristiano Galbiati on the Wimp Argon Programme, for which I spent a summer in the beautiful town of L’Aquila, Italy. Cristiano has always believed in my work, and I am very grateful for having him as my mentor. Finally, I would like to thank my family for their unconditional love. In particular for my parents: I deeply appreciate your support for your son’s career in a faraway land. I hope that I will see you again soon. v Contents Abstract iii Acknowledgements iv Contents vi List of Figures ix List of Tables xxi 1 Introduction 1 1.1 Dynamicsoftheuniverse . 1 1.2 Constituents of the universe and distance measures . .......... 4 1.3 Inflation...................................... 6 1.4 Acceleratedexpansionanddarkenergy. ...... 8 1.5 PrimaryanisotropiesoftheCMB . 10 1.6 Sunyaev-Zel’dovich effect, CMB polarization, lensing . ........... 14 1.6.1 TheSunyaev-Zel’dovicheffect . 14 1.6.2 WeaklensingandCMBpolarization . 16 1.7 The Atacama Cosmology Telescope . 18 1.8 Overview ..................................... 19 2 Ideal TES bolometer theory 21 2.1 Superconductors as thermal detectors . ...... 21 2.2 Small signal theory for the ideal TES; responsivity calculation . 25 vi 2.3 Noisecalculation ................................ 29 2.3.1 Some mathematical definitions; Gaussian and white noise ...... 29 2.3.2 Thermalfluctuationnoise . 32 2.3.3 TESJohnsonnoise............................ 33 2.3.4 Load (shunt) resistor Johnson noise . 35 2.4 Compleximpedance ............................... 36 3 Dark measurements of ACT TES bolometers 38 3.1 TES column assemblies and dark measurements . ...... 38 3.2 Current readout calibration; open and closed loop measurements . 41 3.2.1 Determintion of Mratio and parasitic resistance . 46 3.3 Calibration of frequency domain measurements . ........ 48 3.3.1 Transferfunctions ............................ 51 3.3.2 Calibration of the load resistor Johnson noise spectrum ....... 52 3.3.3 Calibration of the TES complex impedance . 55 3.3.4 Calibration of the TES noise spectrum . 57 3.3.5 Asymmetry between the calibration of the complex impedance and thenoisespectrum ............................ 60 3.4 Periodogram analysis of Johnson noise . ...... 60 3.5 Improved periodogram analysis of Johnson noise . ........ 65 3.5.1 Periodogramaveraging. 66 3.5.2 Periodogramwindowing . 66 3.6 Estimating load resistances from Johnson noise . ......... 69 3.6.1 Calibration of ROX2 resistance-temperature correspondences from ROX1................................... 71 3.7 Current-voltage characteristic (I-V curve) measurements . 72 4 Characterization of thermal architectures of ACT TES bolometers 77 4.1 Simple calculations of electrical and thermal properties of ACT TES bolometers 79 4.1.1 Heatcapacities .............................. 79 4.1.2 Thermalconductances . 81 vii 4.2 ModelingACTTESbolometers. 84 4.2.1 Compleximpedance ........................... 88 4.2.2 Noisederivation ............................. 88 4.3 TESbolometersformodeling . 91 4.4 Dataacquisitionandanalysis . 93 4.5 Results,robustnessoffits . 99 4.6 Alternativemodel ................................ 113 4.7 Conclusion .................................... 118 5 Possible explanations for anomalous ACT TES bolometer behaviors 121 5.1 The thermal conductance from the MoAu bilayer to the silicon substrate . 122 5.2 Possible limitations of the model . 125 5.3 Anomalousheatcapacities. 126 5.4 Suggestions for further characterization measurements and future TES designs127 References 130 viii List of Figures 1.1 Various CMB power spectra from theoretical prediction: the temperature power spectrum (TT, in blue), the EE polarization power spectrum (ma- genta), the BB polarization spectra at two different tensor-to-scalar ratios (r = 0.01 and r = 0.10, in black), and the contribution to BB polariza- tion from lensing-converted EE polarization (red). The XX power spec- trum refers to the correlation of the field X with itself, such as that de- fined in Equation 1.12, where the field X can be the temperature field, the E-mode polarization field, or the B-mode polarization field here (see Sec- tion 1.6.2). More generally, the XY power spectrum refers to the correlation of the field X with the field Y. The cosmic variance for the temperature power spectrum is also shown (dashed blue). The data plotted assumes τ(the optical depth) = 0.1 and nS(the scalar spectral index) = 0.96. Figure courtesy of Thomas Essinger-Hileman. 12 2.1 The electrothermal circuit of an ideal TES. A typical electrical circuit with readout is shown on the left, and its Thevenin equivalent circuit is shown in the middle. The thermal circuit is shown on the right. ...... 25 ix 3.1 An ACT TES column assembly sitting in a (partial) copper carrier. The different components of the column assembly are labeled in the figure. The copper carrier is used in the SRDP testing and is not installed in the MBAC, where the column assemblies are closely stacked together. The ROX1, not shown in this figure, is attached to the copper carrier. The ROX2 is glued ontothesiliconcircuitboard. 39 3.2 Simplified SRDP testing setup. Please refer to the text for detailed descriptions. 42 3.3 SRDP open loop measurements to determine Mratio, the ratio of the input inductance to the feedback inductance. In this figure, the SQUID readout VSQ as we sweep the current through the TES is drawn in blue, and the readout as we sweep the current through the feedback line is drawn in red.