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N. Mast, Cryogenic Detector Development for SuperCDMS, Ph.D. Thesis, University of Minnesota
We then present some work related to reconstruction of event position in the detectors, including new analysis techniques and a novel cryogenic calibration source mover we have developed and tested. We also present tests of improving experimental scalability by increasing individual detector masses using the largest-diameter cryogenic Si detectors yet operated. We present first experimental results from the novel use of (n,$\gamma$) processes to calibrate the low energy nuclear recoil energy scale. This work is essential to understand how DM-nuclear interactions will manifest in semiconductor detectors. We also take a short look at the newest, most sensitive detectors currently operated by SuperCDMS and discuss how they are allowing new insights into critical physics processes in all SuperCDMS detectors. Finally, we demonstrate how some of the various improvements discussed in this work can improve the experimental reach of the next generation of SuperCDMS at SNOLAB.
L. Bezerra, SuperCDMS Event Reconstruction Using Convolutional Neural Networks, MSc. Thesis, University of British Columbia
This thesis first describes the integration of a new Signal Distribution Unit (SDU) to the SuperCDMS data acquisition system, which allows for synchronization of multiple detectors and electronic/mechanical noise characterization via accelerometer, antenna, and AC phase measurements.
From SuperCDMS detector data it is necessary to reconstruct the energies of the particle events. This thesis explores the use of Convolutional Neural Networks (CNNs) to perform this reconstruction and finds that, although they perform well, changing the noise model breaks the model and requires the neural network to be retrained. In order to mitigate this issue, a new CNN model is proposed which includes the noise Power Spectral Density (PSD) of the data as an additional input to the CNN. While it proves to be effective as a denoising algorithm, it still fails for data with a different noise model. However, including data from multiple PSDs in the neural network training sample allows it to handle data with different types of noise while still maintaining the quality of the reconstruction. Nevertheless, neural networks trained even on multiple PSDs do not robustly handle data taken with PSDs dissimilar to those in the training sample, suggesting that CNNs may need to be retrained whenever the noise environment changes in a significant way.
J. Morales, Simulation of Dark Matter and Standard Model Interactions in the SuperCDMS Soudan Experiment, Ph. D Thesis, TAMU
M. Bowles, Minimizing Backgrounds for the SuperCDMS SNOLAB Dark-Matter Experiment, Ph.D Thesis, South Dakota School of Mines and Technology
Backgrounds from the progeny decay of the abundant, naturally-occurring radioactive isotope radon-222 obstruct the sensitivity of essentially every dark-matter search. Radon concentrations in the Snolab cavern would contribute prohibitively large backgrounds if the volume surrounding the detectors were not purged with a low-flow low-radon gas. By measuring the radon diffusion and emanation, we identified acceptable gasket materials for sealing this radon purge, ensuring that the radon-induced backgrounds will be significantly lower than the other experimental backgrounds. A radon emanation system with a gas handling system and low-background radon detector was commissioned and used to measure the radon emanation of the proposed gaskets. A low-cost apparatus was constructed to measure the radon diffusion of gaskets with a commercial radon detector.
The sensitivity of future generations of dark-matter detectors are expected to be dominated by long-lived low-energy beta- and alpha-emitting radon daughters such as 210 Pb on detector surfaces. I describe simulations indicating the detector could also be used to reduce background from material impurities plaguing rare-event searches, the commissioning of a prototype demonstration detector, and a gas handling system necessary to operate the detector. I demonstrated that the gas handling system reduces the otherwise dominant backgrounds by a factor of 62. This detector will therefore be able to detect 32 Si and 210 Pb 100 times better than currently available screeners.
M. Matheny, The Effect of Ionization Variance on Nuclear-Recoil Dark Matter Searches, M.Sc Thesis, University of Colorado Denver
Previous simulations have shown that we do not entirely understand the ionization efficiency (yield) for electron and nuclear recoils, as the assumption that the distribution for the yield is normally distributed for a true recoil energy is violated. Since the yield distribution may directly affect dark matter low-mass limits, it is crucial we understand how the yield is distributed.
A component to understanding the yield distribution is the variance in the number of electron-hole pairs produced or ionization variance. This effect has been studied relatively infrequently as experiments have been interested in large energy deposits (10 - 100 keV) and could accurately separate electron and nuclear recoil events. For electron recoils, the ionization variance is described by a “Fano” factor. For nuclear recoils the effect can be parameterized by an “effective” Fano factor, which has similar definition but a different physical origin. The nuclear recoil “effective” Fano factor is shown to be much larger than the electron-recoil version above around 10 keV deposited energy
D. Jardin, A Likelihood Search for Low-mass Dark Matter via Inelastic Scattering in SuperCDMS, Ph. D. Thesis, SMU
The properties of dark matter have yet to be identified, thus efforts are ongoing to explore a range of possible masses and interaction cross-sections. For the latter, experiments can increase exposure by scaling up the detector mass and operating for a longer time. To search for dark matter with less mass than a nucleon, new technologies and analysis techniques need to be developed to be sensitive to energy deposits less than a few keV.
SuperCDMS is a direct detection experiment that measures ionization and phonon energy in cryogenic germanium crystal detectors. A special mode of operating the SuperCDMS detectors, called CDMSlite, amplifies the ionization signal via phonon creation. This amplification leads to a lower energy threshold, which provides sensitivity to smaller dark matter masses.
Typically, direct detection experiments assume dark matter scatters elastically off the nuclei in the detector. In this thesis, I will highlight the most recent CDMSlite elastic dark matter search. Then I will describe how inelastic dark matter collisions can manifest in the detector and be useful for extending experimental sensitivity to lower dark matter masses. Finally, I will present a re-analysis of CDMSlite data using a profile likelihood to search for low-mass dark matter through two inelastic scattering channels: Bremsstrahlung radiation, and the Migdal Effect.
B. Page, Searching for low-mass dark matter with SuperCDMS Soudan detectors, Ph. D. Thesis, University of British Columbia
H. Rogers, Effective Field Theory Analysis and Active Neutron Veto Design for the Cryogenic Dark Matter Search , Ph.D. Thesis, University of Minnesota
The scattering of dark matter particles off nuclei in direct detection experiments can be described in terms of a multidimensional effective field theory (EFT). A new systematic analysis technique is developed using the EFT approach and Bayesian inference methods to exploit, when possible, the energy-dependent information of the detected events, experimental efficiencies, and backgrounds. Highly dimensional likelihoods are calculated over the mass of the weakly interacting massive particle (WIMP) and multiple EFT coupling coefficients, which can then be used to set limits on these parameters and choose models (EFT operators) that best fit the direct detection data. Expanding the parameter space beyond the standard spin-independent isoscalar cross section and WIMP mass reduces tensions between previously published experiments. Combining these experiments to form a single joint likelihood leads to stronger limits than when each experiment is considered on its own. Simulations using two nonstandard operators (O3 and O8) are used to test the proposed analysis technique in up to five dimensions and demonstrate the importance of using multiple likelihood projections when determining constraints on WIMP mass and EFT coupling coefficients. In particular, this shows that an explicit momentum dependence in dark matter scattering can be identified.
CDMSlite Run 2 was a search for Weakly Interacting Massive Particles (WIMPs) with a cryogenic 600 g Germanium detector operated deep underground. It was operated in a mode optimizing sensitivity to WIMPs of relatively low mass, 2 - 20 GeV, while sacrificing background rejection. An EFT analysis of CDMSlite Run 2 data from SuperCDMS Soudan is presented here. A binned likelihood Bayesian analysis was performed on the data, optimizing over the parameters of EFT interactions and the recoil energy spectra due to the dominant Compton scattering and tritium backgrounds. Recoil energy regions within 5σ of known activation peaks were removed from the analysis. The Bayesian evidences of the resulting likelihoods show that CDMSlite Run 2 data is entirely consistent with the background models with no EFT interaction necessary. Upper limits on the WIMP mass and coupling coefficients amplitudes and phases are presented for each EFT operator.
B. Cornell, A Dark Matter Search Using the Final SuperCDMS Soudan Dataset and the Development of a Large-Format, Highly-Multiplexed, Athermal-Phonon-Mediated Particle Detector, Ph.D. Thesis, CalTech
The first part focuses on the blinded analysis of roughly three years of data collected from March 2012 to November 2015 by the SuperCDMS Soudan experiment. SuperCDMS Soudan consists of an array of 15, 0.6-kg, cryogenic, Ge iZIP particle detectors situated in a decommissioned iron mine in remote northern Minnesota. This analysis is optimized to be sensitive to theoretical WIMP masses above 10 GeV/c2. This result set the strongest limits for WIMP--germanium-nucleus interactions for WIMP masses greater than 12 Gev/c2.
The second part focuses on the development new kind of particle detector in the style of a SuperCDMS iZIP, designed to simplify fabrication and readout, improve phonon-based position reconstruction, and help to scale to larger target arrays. These detectors replace the TES-based phonon sensors of the iZIP with Microwave Kinetic Inductance Detectors (MKIDs).
M. Stein, An Analysis of Frenkel Defects and Backgrounds Modeling for SuperCDMS Dark Matter Searches, Ph. D. Thesis, SMU
N. Kurinsky, The Low-Mass Limit: Dark Matter Detectors With eV-Scale Energy Resolution, Ph.D. Thesis, Department of Physics, Stanford University
D. Barker, SuperCDMS Background Models for Low-Mass Dark Matter Searches, Ph.D. Thesis, Department of Physics, University of Minnesota
Multiple new models were developed for detectors operated in CDMSlite at Soudan. These include the analytical formula for Compton scattering, and empirical models for surface backgrounds from 210Pb contamination of the germanium crystals and detector housing. In order to accurately describe the surface events, a new detector response function was developed that included information about the electric field and energy resolution of the detector. These models were essential to the implementation of a profile likelihood analysis of the CDMSlite Run 3 data, which improved on the sensitivity to dark matter over the Run 2 optimum interval analysis for WIMP masses above 2.5 GeV/c2. This demonstrated a successful application of a likelihood analysis to the high-voltage operating mode, and the potential for these analyses in the future SuperCDMS SNOLAB experiment.
M. Daal, Kinetic Inductance Detectors for Dark Matter Searches, Ph.D. Thesis, Department of Physics, University of California, Berkeley
This instrumentation focused thesis shows that KIPS can be used as a simple and sensitive phonon sensor for the CDMS detector. KIPS design aspects, competitiveness to the current transition edge phonon sensors, readout considerations and suggestions on how to instrument them in future dark matter experiments will be presented. The broader applicability of KIPS in nuclear non-proliferation and other physics investigations is also discussed.
D. Speller, A Background-Subtracted Search for Annual Modulation in CDMS II, Ph.D. Thesis, Department of Physics, University of California, Berkeley
This work describes a background-subtracted search for annual modulation in the WIMP- search data acquired in the Cryogenic Dark Matter Search II (CDMS II) Experiment, which was the second implementation of the highly successful CDMS technology. We observe no significant modulation in the 2.7 keVnr to 11.9 keVnr (nuclear-recoil-equivalent) energy range selected for this analysis. These results are not compatible with a WIMP dark matter interpretation of the signals reported by the DAMA/LIBRA and CoGeNT experiments, and provide complementary support to earlier CDMS low-threshold germanium analyses.
A. Kennedy, Simulating The Supercdms Dark Matter Detector Response And Readout, Ph.D. Thesis, Department of Physics, University of Minnesota
As part of detector R&D, the Minnesota test facility also looks beyond the next stage of SuperCDMS, investigating larger individual detectors as a means to easily scale up the sensitive mass of future searches. This thesis presents the design and initial testing results of a prototype 150 mm diameter, 33 mm thick silicon ionization detector, which is 5.2 times larger than those used in SuperCDMS at Soudan and 2.25 times larger than those planned for use at SuperCDMS SNOLAB. In addition, the detector was operated with contact-free ionization electrodes to minimize bias leakage currents, which can limit operation at high bias voltages. The results show promise for the operation of both large volume silicon detectors and contact-free ionization electrodes for scaling up detector mass and bias.
H. Qiu, A Search For Weakly Interacting Massive Particles Utilizing A Profile Likelihood Ratio Technique With The Supercdms Soudan Experiment, Ph.D. Thesis, Department of Physics, Southern Methodist University
Neutrons are the most dangerous background in a direct dark matter search experiment. The nuclear recoil signal that a neutron produces in a Ge detector is indistinguishable from that a WIMP produces. Protection against them is one of the key aspects for the next generation of SuperCDMS experiment at SNOLAB. An active neutron veto system was proposed to be implemented in this future experiment to make it more robust from neutrons. The feasibility of both the plastic and liquid neutron veto systems was studied.
R. Agnese, Simulating The Supercdms Dark Matter Detector Response And Readout, Ph.D. Thesis, Department of Physics, University of Florida
This work describes the design and implementation of a low temperature condensed matter physics simulation library built on top of the popular Geant4 particle tracking framework. The library, named “Geant4 Condensed Matter Physics” or G4CMP, intro- duces several solid state concepts to the Geant4 framework such as crystal lattices, phonon quasiparticles, non-scalar effective masses, and implements several physics processes relevant to cryogenic temperature crystals.
In addition to the physics library, which is intended for general use, this work also describes a full Monte Carlo simulation package for the SuperCDMS iZIP detectors which utilizes G4CMP at its core and also fully simulates the detector readout sensors.
T. Binder, A Study of Charge Propagation and Quantification of Noise Within the SuperCDMS Detector, M.Sc Thesis, Department of Physics, University of South Dakota
M. Pepin, Low-Mass Dark Matter Search Results and Radiogenic Backgrounds for the Cryogenic Dark Matter Search, Ph.D. Thesis, Department of Physics, University of Minnesota
Y. Chen, High-Energy Neutron Backgrounds For Underground Dark Matter Experiments, Ph.D. Thesis, Department of Physics, Syracuse University
M. Penalver Martinez, Neutron background estimation for direct WIMP searches at SuperCDMS Soudan, M.Sc Thesis, Department of Physics, University of Durham
A. Phipps, Ionization Collection in Detectors of the Cryogenic Dark Matter Search, Ph.D. Thesis, Department of Physics, University of California, Berkeley
R. Moffatt, Two-Dimensional Spatial Imaging of Charge Transport in Germanium Crystals at Cryogenic Temperatures, Ph.D. Thesis, Department of Physics, Stanford University
This asymmetry is a consequence of the anisotropic propagation of electrons in germanium at cryogenic temperatures. To better model our detectors, we incorporated this effect into our Monte Carlo simulations of charge transport. The purpose of the experiment described in this dissertation is to test those models in detail.
Our measurements have allowed us to discover a shortcoming in our most recent Monte Carlo simulations of electrons in germanium. This discovery would not have been possible without the measurement of the full, two-dimensional charge distribution, which our experimental apparatus has allowed for the first time at cryogenic temperatures.
B. Page, Data acquisition for SuperCDMS SNOLAB, M.Sc Thesis, Department of Physics, University of British Columbia
B. Welliver, Dedicated Searches For Low And High Mass Wimps With The SuperCDMS Soudan iZIP Detectors, Ph.D. Thesis, Department of Physics, University of Florida
Effort is to extend the analysis to higher masses require long running times during which many aspects of the detectors or the environment can change. Additional challenges are offered by the powerful background discrimination ability of the iZIP. The background distributions are well separated from the signal region, meaning most of the leakage arises from low-probability tails of the background distributions. In the absence of an enormous dataset, extrapolations from the bulk of the distribution are required. While attempting to obtain a model of gamma induced electron-recoils leaking into the signal region of the detector from high radius a curious asymmetry between the sides of the detectors was discovered potentially indicating an electronics or detector design problem.
A. Jastram, CDMS Detector Fabrication Improvements And Low Energy Nuclear Recoil Measurements In Germanium, Ph.D. Thesis, Department of Physics, Texas A&M University
Additionally, as the dark matter parameter space is probed further, careful calibrations of detector response to nuclear recoil interactions must be performed in order to extract useful information (in relation to dark matter particle characterizations) from experimental results. A neutron beam of tunable energy is used in conjunction with a commercial radiation detector to characterize ionization energy losses in germanium during nuclear recoil events. Data indicates agreement with values predicted by the Lindhard equation, providing a best-fit k-value of 0.146.
J. Yen, Phonon Sensor Dynamics For Cryogenic Dark Matter Search Experiment: A Study Of Quasiparticle Transport In Aluminum Coupled To Tungsten Transition Edge Sensors, Ph.D. Thesis, Department of Physics, Stanford University
K. Schneck, Search For Low-Mass Dark Matter With Supercdms Soudan And Study Of Shorted Electric Field Configurations In CDMS Detectors, Ph.D. Thesis, Department of Physics, Stanford University
In addition, a few SuperCDMS Soudan detectors experienced cold hardware problems that can affect the data collected. Of particular interest is one detector considered for the low-mass WIMP search that has one of its charge electrodes shorted to chassis ground. Three events were observed in this detector upon unblinding the SuperCDMS Soudan low-energy data, even though <1 event was expected based on pre-unblinding calulations. However, the data collected by the shorted detector may have been compromised since an electrode shorted to ground will modify the electric field in the detector. The SuperCDMS Detector Monte Carlo (DMC) provides an excellent way to model the effects of the modified electric field, so a new model of the expected backgrounds in the low-mass WIMP search is developed using the DMC to try to explain how the short may have affected the data collected.
A.J. Anderson, A Search for Light Weakly-Interacting Massive Particles with SuperCDMS and Applications to Neutrino Physics, Ph.D. Thesis, Department of Physics, MIT
Cryogenic detectors similar to SuperCDMS also have potential applications in neutrino physics. We study several configurations in which dark matter detectors could be used with an intense neutrino source to detect an unmeasured Standard Model process called coherent neutrino scattering. This process may be useful, for example, as a calibration for next-generation dark matter detectors, and for constraining eV-scale sterile neutrinos. In addition, small cryogenic X-ray detectors on sounding rockets with large fields-of-view have the unique ability to constrain sterile neutrino dark matter. We set limits on sterile neutrino dark matter using an observation by the XQC instrument, and discuss prospects for a future observation of the galactic center using the Micro-X instrument.
S.M. Fallows, Measurement of Nuclear Recoils in the CDMS II Dark Matter Search , Ph.D. Thesis, Department of Physics, University of Minnesota
Nuclear recoils have suppressed ionization signals relative to electron recoils of the same recoil energy, so the response of the detectors is calibrated differently for each recoil type. ...
I discuss systematic uncertainties affecting the reconstruction of this recoil energy, the primary analysis variable, and use several methods to constrain their magnitude. I present the resulting adjusted WIMP limits and discuss their impact in the context of current and projected constraints on the parameter space for WIMP interactions.
R. Basu Thakur, The Cryogenic Dark Matter Search Low Ionization-Threshold Experiment , Ph.D. Thesis, Department of Physics, University of Illinois at Urbana-Champaign
T. Hofer, Development of CDMS-II Surface Event Rejection Techniques and Their Extensions to Lower Energy Thresholds , Ph.D. Thesis, Department of Physics, University of Minnesota
A full re-analysis of the CDMS-II data was motivated by an improvement in the event reconstruction algorithms which improved the resolution of ionization energy and timing information. The Ge data were re-analyzed using three distinct background-rejection techniques; the Si data from runs 125 - 128 were analyzed for the first time using the most successful of the techniques from the Ge re-analysis. The results of these analyses prompted a novel “mid-threshold” analysis, wherein energy thresholds were lowered but background rejection using phonon timing information was still maintained. This technique proved to have significant discrimination power, maintaining adequate signal acceptance and minimizing background leakage.
J. Zhang, A Dark Matter Search Using the Final CDMS-II Data and 100 mm SuperCDMS Germanium Detector Ionization Test, Ph.D. Thesis, Department of Physics, University of Minnesota
The data taken during the last four runs of CDMS II with total raw exposure 612 kg-day were reprocessed with improved ionization pulse reconstruction algorithm. We present the classic timing analysis with the reprocessed data in this thesis. For the four runs combined, this analysis resulted in a new WIMP-nucleon cross section 4.4×10-44 cm2 for a WIMP mass of 70 GeV/c2, which is a factor of 1.6 improvement compared to the original c58 classic timing analysis.
B. Shank, Testing And Characterization Of Supercdms Dark Matter Detectors, Ph.D. Thesis, Department of Physics, Stanford University
K. Prasad, Search for lightly ionizing particles using CDMS-II data and fabrication of CDMS detectors with improved homogeneity in properties, Ph.D. Thesis, Department of Physics, Texas A&M University
The Cryogenic Dark Matter Search (CDMS-II), located at Soudan mines in northern Minnesota, employs germanium and silicon crystals to perform direct searches for a leading candidate to dark matter called Weakly Interacting Massive Particles (WIMPs). Alternately, the low detection threshold allows search for fractional electromagnetic-charged particles, or Lightly Ionizing Particles (LIPs), moving at relativistic speed. Background rejection is obtained by requiring that the magnitude and location of energy deposited in each detector be consistent with corresponding "signatures" resulting from the passage of a fractionally charged particle. In this dissertation, the CDMS-II data is analyzed to search for LIPs, with an expected background of 0.078±0.078 events. No candidate events are observed, allowing exclusion of new parameter space for charges between e/6 and e/200. ...
K. Page, A modified detector concept for SuperCDMS: The HiZIP and its charge performance, M.Sc Thesis, Department of Physics, Queen's University Kingston ON, Canada
SuperCDMS currently operates about 9 kg of Ge detectors at the Soudan underground lab in northern Minnesota. In its next phase, SuperCDMS SNOLAB plans to use 100-200 kg of target mass (Ge) which would allow it to probe more of the interesting and as of yet unexplored parameter space for WIMPs predicted by theoretical models. The SuperCDMS Queen's Test Facility is a detector test facility which is intended to serve for detector testing and detector research and development purposes for the SuperCDMS experiment.
A modied detector called the `HiZIP' (Half-iZIP), which is reduced in complexity in comparison to the currently used iZIP (interleaved Z-sensitive Ionization and Phonon mediated) detectors, is studied in this thesis. ...
K. McCarthy, Detector Simulation and WIMP Search Analysis for the Cryogenic Dark Matter Search Experiment, Ph.D. Thesis, Department of Physics, Massachusetts Institute of Technology
The Cryogenic Dark Matter Search (CDMS) collaboration aims to detect the scattering of WIMP particles from nuclei in terrestrial detectors. Germanium and silicon particle detectors are deployed in the Soudan Underground Laboratory in Minnesota. These detectors are instrumented with phonon and ionization sensors, which allows for discrimination against electromagnetic backgrounds, which strike the detector at rates orders of magnitude higher than the expected WIMP signal.
This dissertation presents the development of numerical models of the physics of the CDMS detectors, implemented in a computational package collectively known as the CDMS Detector Monte Carlo (DMC). After substantial validation of the models against data, the DMC is used to investigate potential backgrounds to the next iteration of the CDMS experiment, known as SuperCDMS. Finally, an investigation of using the DMC in a reverse Monte Carlo analysis of WIMP search data is presented. ...
J. Kiveni, A Search for WIMP Dark Matter using an Optimized Chi-square Technique on the Final Data from the Cryogenic Dark Matter Search Experiment (CDMS II) , Ph.D. Thesis, Department of Physics, Syracuse University
This analysis achieved the best expected sensitivity of the three techniques developed for the reanalysis and so was chosen as the primary timing analysis whose limit will be quoted in a on-going publication paper which is currently in preparation. For this analysis, a total raw exposure of 612.17 kg-days are analyzed for this work. No candidate events was observed, and a corresponding upper limit on the WIMP-nucleon scattering cross section as a function of WIMP mass is defined. These data set a 90% upper limit on spin-independent WIMP-nucleon elastic-scattering cross section of 3.19×10-44 cm2 for a WIMP mass of 60 GeV/c2. Combining this result with all previous CDMS II data gives an upper limit of 1.96×10-44 cm2 for a WIMP of mass 60 GeV/c2 (a factor of 2 better than the original analysis). ...
S. Hertel, Advancing the Search for Dark Matter: from CDMS II to SuperCDMS, Ph.D. Thesis, Department of Physics, Massachusetts Institute of Technology
This thesis describes two such experimental efforts: CDMS II (2007-2009) and SuperCDMS Soudan (ongoing). The general abilities and sensitivities of both experiments are laid out, placing a special emphasis on the detector technology, and how this technology has evolved from the first to the second experiment. Some topics on which I spent significant efforts are described here only in overview (in particular the details of the CDMS II analysis, which has been laid out many times before), and some topics which are not described elsewhere are given a somewhat deeper treatment.
In particular, this thesis is hopefully a good reference for those interested in the annual modulation limits placed on the low-energy portion of the CDMS II exposure, the design of the detectors for SuperCDMS Soudan, and an overview of the extremely informative data these detectors produce. It is an exciting time. The technology I've had the honor to work on the past few years provides a wealth of information about each event, more so than any other direct detection experiment, and we are still learning how to optimally use all this information. Initial tests from the surface and now underground suggest this technology has the background rejection abilities necessary for a planned 200kg experiment or even ton-scale experiment, putting us on the threshold of probing parameter space orders of magnitude from where the field currently stands.
D. Moore, A Search for Low-Mass Dark Matter with the Cryogenic Dark Matter Search and the Development of Highly Multiplexed Phonon-Mediated Particle Detectors, Ph.D. Thesis, Division of Physics, Mathematics & Astronomy, California Institute of Technology
The Cryogenic Dark Matter Search (CDMS II) attempts to identify WIMP interactions using an array of cryogenic germanium and silicon particle detectors located at the Soudan Underground Laboratory in northern Minnesota. In this dissertation, data taken by CDMS II are reanalyzed using a 2 keV recoil energy threshold to increase the sensitivity to WIMPs with masses ∼10 GeV. These data disfavor an explanation for the DAMA/LIBRA, CoGeNT, and CRESST-II results in terms of spin-independent elastic scattering of WIMPs with masses ~12 GeV, under standard assumptions. At the time of publication, they provided the strongest constraints on spin-independent elastic scattering from 5-9 GeV, ruling out previously unexplored parameter space. ...
M. Pyle, Optimizing the Design and Analysis of Cryogenic Semiconductor Dark Matter Detectors for Maximum Sensitivity, Ph.D. Thesis, Department of Physics, Stanford University
Due to electronic carrier trapping at the surface of our semiconductor crystals, electron recoils which occur near the surface have suppressed ionization measurements and can not be distinguished from WIMP induced nuclear recoils and thus sensitivity to the WIMP nucleon interaction cross section was driven in CDMS II by our ability to define a full 3D fiducial volume in which all events had full collection. To remain background free and maximally sensitive to the WIMP-nucleus interaction cross section, we must improve our 3D fiducial volume definition at the same rate as we scale the mass of the detector, and thus proposed next generation experiments with an order of magnitude increase in active mass were unfortunately not possible with our previous CDMS II detector design, and a new design with significantly improved fiducialization performance is required.
K.M. Sundqvist, Carrier Transport and Related Effects in Detectors of the Cryogenic Dark Matter Search, Ph.D. Thesis, Department of Physics, University of California, Berkeley
By simultaneously measuring signals from deposited charge and the energy in nonequilibrium phonons created by particle interactions in intrinsic germanium crystals at a temperature of 40 mK, a signature response for each event is produced. This response, combined with phonon pulse-shape information, allows CDMS to actively discriminate candidate WIMP interactions with nuclei from electromagnetic radioactive background which interacts with electrons.
Z. Ahmed, A Dark-Matter Search Using the Final CDMS II Dataset and a Novel Detector of Surface Radiocontamination, Ph.D. Thesis, Division of Physics, Mathematics & Astronomy, California Institute of Technology
Interactions of WIMPs with baryons are expected to be rare, but might be detectable in low-noise detectors. The Cryogenic Dark Matter Search (CDMS) experiment uses ionizationand phononsensitive germanium particle detectors to search for such interactions. CDMS detectors are operated at the Soudan Underground Laboratory in Minnesota, within a shielded environment to lower cosmogenic and radioactive background. The combination of phonon and ionization signatures from the detectors provides excellent residual-background rejection.
R. Bunker, A Low-threshold Analysis of Data from the Cryogenic Dark Matter Search Experiment, Ph.D. Thesis, Department of Physics, University of California Santa Barbara
An incontrovertible positive detection has remained elusive. However, a few experiments have recorded data that appear consistent with a low-mass WIMP. This thesis describes an attempt to probe the favored parameter space. To increase sensitivity to low-mass WIMPs, a low-threshold technique with improved sensitivity to small energy depositions is applied to CDMS shallow site data. Four germanium and two silicon detectors were operated between December 2001 and June 2002, yielding 118 days of exposure. By sacrificing some of the CDMS detectors ability to discriminate signal from background, energy thresholds of ~1 and ~2 keV were achieved for three of the germanium and both silicon detectors, respectively. A large number of WIMP candidate events are observed, most of which can be accounted for by misidentification of background sources. No conclusive evidence for a low-mass WIMP signal is found. The observed event rates are used to set upper limits on the WIMP-nucleon scattering cross section as a function of WIMP mass. Interesting parameter space is excluded for WIMPs with masses below ~9GeV/c2. Under standard assumptions, the parameter space favored by interpretations of other experiments data as low-mass WIMP signals is partially excluded, and new parameter space is excluded for WIMP masses between 3 and 4 GeV/c2.
M. Fritts, Background Characterization and Discrimination in the Final Analysis of the CDMS II Phase of the Cryogenic Dark Matter Search, Ph.D. Thesis, School of Physics and Astronomy, University of Minnesota
We seek collisions between WIMPs and atomic nuclei in disk-shaped germanium and silicon detectors. A key design feature is to keep the rate of collisions from known particles producing WIMP-like signals very small. The largest category of such background is interactions with electrons in the detectors that occur very close to one of the faces of the detector. The next largest category is collisions between energetic neutrons that bypass the experimental shielding and nuclei in the detectors. Analytical efforts to discriminate these backgrounds and to estimate the rate at which such discrimination fails have been refined and improved throughout each phase of CDMS.
Next-generation detectors for future phases of CDMS require testing at cryogenic test facilities. One such facility was developed at the University of Minnesota in 2007 and has been used continuously since then to test detectors for the next phase of the experiment, known as SuperCDMS.
T. Bruch, A Search for Weakly Interacting Particles with the Cryogenic Dark Matter Search Experiment, Ph.D. Thesis, Department of Physics, University of Zurich
In the standard model of disc galaxy formation, a dark matter disc forms as massive satellites are preferentially dragged into the disc-plane and dissolve. The low velocity of the dark matter particles in the dark disc with respect to the Earth enhances detection rates at low recoil energy in direct detection experiments. For WIMP masses &50GeV/c2, the detection rates increase by up to a factor of 3 in the 5-20 keV recoil energy range. Comparing this with rates at higher energies may be sensitive to the WIMP mass, providing stronger mass constraints particularly for masses ~100GeV/c2. The annual modulation signal is significantly boosted and the modulation phase is shifted by ~3 weeks relative to the dark halo. The variation of the observed phase with recoil energy determines the particle's mass, once the dark disc properties are fixed by future astronomical surveys. ...
X. Qiu, Advanced Analysis and Background Techniques for the Cryogenic Dark Matter Search, Ph.D. Thesis, Department of Physics, University of Minnesota
C.N. Bailey, The Cryogenic Dark Matter Search: First 5-Tower Data and Improved Understanding of Ionization Collection, Ph.D. Thesis, Department of Physics, Case Western Reserve University
As CDMS aims to achieve greater WIMP sensitivity, it is necessary to increase the detector mass and discrimination between signal and background events. Incomplete ionization collection results in the largest background in the CDMS detectors as this causes electron recoil background interactions to appear as false candidate events. Two primary causes of incomplete ionization collection are surface and bulk trapping.
Recent work has been focused on reducing surface trapping through the modification of fabrication methods for future detectors. Analyzing data taken with test devices has shown that hydrogen passivation of the amorphous silicon blocking layer worsens surface trapping. Additional data has shown that the iron-ion implantation used to lower the critical temperature of the tungsten transition-edge sensors causes a degradation of the ionization collection. Using selective implantation on future detectors may improve ionization collection for events near the phonon side detector surface. ...
J.P. Filippini, A Search for WIMP Dark Matter Using the First Five-Tower Run of the Cryogenic Dark Matter Search, Ph.D. Thesis, Department of Physics, University of California, Berkeley
The Cryogenic Dark Matter Search (CDMS) experiment seeks to directly detect the rare elastic interactions of galactic WIMPs with terrestrial nuclei. To this end, CDMS operates an array of crystalline Ge and Si particle detectors in Soudan Underground Laboratory in northern Minnesota. These crystals are operated at millikelvin temperatures and instrumented to measure the ionization and athermal phonons generated by each particle interaction. This combination provides a powerful two-fold discrimination against the interactions of particles generated by radioactive decay and cosmogenic showers.
This dissertation describes the commissioning, analysis, and results of the first WIMP-search data runs of the CDMS experiment with its full complement of 5 "Towers" of detectors. These data represent a substantial increase in target mass and exposure over previous CDMS results. The results of this work place the most stringent limits yet set upon the WIMP-nucleon spin-independent cross section for WIMP masses above ~ 44 GeV/c2, as well as setting competitive limits on spin-dependent WIMP-nucleon interactions. This work also outlines the larger context of this and other probes of the WIMP theory of dark matter, as well as some current development efforts toward a larger cryogenic experiment.
R. Hennings-Yeomans, First 5 Tower WIMP-Search Results from the Cryogenic Dark Matter Search with Improved Understanding of Neutron Backgrounds and Benchmarking, Ph.D. Thesis, Department of Physics, Case Western Reserve University
This thesis presents the first 5 tower WIMP-search results from CDMS-II, an estimate of the cosmogenic neutron backgrounds expected at the Soudan Underground Laboratory, and a proposal for a new measurement of high-energy neutrons underground to benchmark the Monte Carlo simulations.
Based on the non-observation of WIMPs and using standard assumptions about the galactic halo , the 90% C.L. upper limit of the spin-independent WIMPnucleon cross section for the first 5 tower run is 6.6 x 10^-44cm2 for a 60 GeV/c2 WIMP mass.
R.W. Ogburn, A search for particle dark matter using cryogenic germanium and silicon detectors in the one- and two-tower runs of CDMS-II at Soudan, Ph.D. Thesis, Department of Physics, Stanford University
The Cryogenic Dark Matter Search (CDMS) seeks to directly detect interactions between WIMPs in the Milky Way's galactic dark matter halo using crystals of germanium and silicon. Our Z-sensitive ionization and phonon ("ZIP") detectors simultaneously measure both phonons and ionization produced by particle interactions. In order to find very rare, low-energy WIMP interactions, we must identify and reject background events caused by environmental radioactivity, radioactive contaminants on the detectors, and cosmic rays. In particular, sophisticated analysis of the timing of phonon signals is needed to eliminate signals caused by beta decays at the detector surfaces. ...
J. Sander, Results from the Crogenic Dark Matter Search Using a Chi Squared Analysis, Ph.D. Thesis, Department of Physics, University of California at Santa Barbara
The CDMS II experiment attempts to detect WIMP interactions in the Soudan Underground Laboratory using germanium detectors and silicon detectors. A WIMP can interact a with detector nuclei causing the nuclei to recoil. A nuclear recoil is distinguished from background electron recoils by comparing the deposited ionization and phonon energies. Electron recoils occurring near detector surfaces are more difficult to reject.
This thesis describes the results of a x^2 analysis designed to reject events occurring near detector surfaces. Because no WIMP signal was observed, separate limits using the germanium and silicon detectors are set on the WIMP cross section under standard astrophysical assumptions.
M.J. Attisha, Cryogenic Dark Matter Search (CDMS-II) - Application of Neural Networks and Wavelets to Event Analysis, Ph.D. Thesis, Department of Physics, Brown University
S. W. Leman, Development Of Phonon-Mediated Transition-Edge-Sensor X-Ray Detectors For Use In Astronomy, Ph.D. Thesis, Department of Physics, Stanford University
The detector uses a large semiconductor absorber and Transition-Edge-Sensors (TESs) to readout the absorbed energy. Calorimetry is performed on individual photons and a partitioning of the energy between various TESs allows for position determination. Hence time varying astronomical sources can be spectroscopically studied and imaged.
A.J. Reisetter, Results from the Two-Tower Run of the Cryogenic Dark Matter Search, Ph.D. Thesis, Department of Physics, University of Minnesota
The ZIP detectors record the ratio of ionization signal to phonon signal to discriminate between nuclear recoils, characteristic of WIMPs and neutrons, and electron recoils, characteristic of gamma and beta backgrounds. They also provide timing information from the four phonon channels that is used to reject surface events, for which ionization collection is poor. A blind analysis, defined using calibration data taken in situ throughout the run, provides a definition of the WIMP signal region by rejecting backgrounds. This analysis applied to the WIMP search data gives a limit on the spin independent WIMP-nucleon cross-section that is an order of magnitude lower than any other experiment has published.
G. Wang, The Cryogenic Dark Matter Search and Background Rejection with Event Position Information, Ph.D. Thesis, Department of Physics, Case Western Reserve University
The Cryogenic Dark Matter Search (CDMS) experiment is searching for evidence of a WIMP interaction off an atomic nucleus in crystals of Ge and Si by measuring simultaneously the phonon energy and ionization energy of the interaction in the CDMS detectors. The WIMP interaction energy is from a few keV to tens of keV with a rate less than 0.1 events/kg/day. To reach the goal of WIMP detection, the CDMS experiment has been conducted in the Soudan mine with an active muon veto and multistage passive background shields.
The CDMS detectors have a low energy threshold and background rejection capabilities based on ionization yield. However, betas from contamination and other radioactive sources produce surface interactions, which have low ionization yield, comparable to that of bulk nuclear interactions. The low-ionization surface electron recoils must be removed in the WIMP search data analysis. An emphasis of this thesis is on developing the method of the surface-interaction rejection using location information of the interactions, phonon energy distributions and phonon timing parameters. The results of the CDMS Soudan run118 92.3 live day WIMP search data analysis is presented, and represents the most sensitive search yet performed.
S. Kamat, Extending the Sensitivity to the Detection of WIMP Dark Matter with an Improved Understanding of the Limiting Neutron Backgrounds, Ph.D. Thesis, Department of Physics, Case Western Reserve University
This thesis describes the effort to understand neutron backgrounds as seen in the two stages of the CDMS search for WIMPs. The first stage of the experiment was at a shallow site at the Stanford Underground Facility where the limiting background came from high-energy neutrons produced by cosmic-ray muon interactions in the rock surrounding the cavern.
Simulations of this background helped inform the analysis of data from an experimental run at this site and served as input for the background reduction techniques necessary to set new exclusion limits on the WIMP-nucleon cross-section, excluding new parameter space for WIMPs of masses 8-20 GeV/c2.
C.L. Chang, The Cryogenic Dark Matter Search (CDMS-II) Experiment - First Results from the Soudan Mine, Ph.D. Thesis, Stanford University
The CDMS II experiment searches for WIMPs via their elastic scattering off of nuclei. The experiment uses Ge and Si ZIP detectors, operated at <50 mK, which simultaneously measure the ionization and athermal phonons produced by the scattering of an external particle. The dominant background for the experiment comes from electromagnetic interactions taking place very close to the detector surface. Analysis of the phonon signal from these interactions makes it possible to discriminate them from interactions caused by WIMPs. This thesis presents the details of an important aspect of the phonon pulse shape analysis known as the Lookup Table Correction. The Lookup Table Correction is a position dependent calibration of the ZIP phonon response which improves the rejection of events scattering near the detector surface. ...
V. Mandic, First Results from the Cryogenic Dark Matter Search Experiment at the Deep Site, Ph.D. Thesis, Department of Physics, University of California, Berkeley
This dissertation presents the commissioning and the results of the first WIMP- search run performed by the CDMS collaboration at the deep underground site at the Soudan mine in Minnesota. We develop different methods of suppressing the dominant background due to the electron-recoil events taking place at the detector surface and we apply these algorithms to the data set. These results place the world's most sensitive limits on the WIMP-nucleon spin-independent elastic-scattering cross-section. Finally, we examine the compatibility of the supersymmetric WIMP-models with the direct-detection experiments (such as CDMS) and discuss the implications of the new CDMS result on these models.
D.D. Driscoll, Development and Performance of Detectors for the Cryogenic Dark Matter Search Experiment with an Increased Sensitivity Based on a Maximum Likelihood Analysis of Beta Contamination, Ph.D. Thesis, Department of Physics, Case Western Reserve University
Contamination of our detectors by a beta emitter can add an unknown source of unrejected background. In the energy range of interest for a WIMP study, electrons will have a short penetration depth and preferentially interact near the surface. Some of the ionization signal can be lost to the charge contacts there and a decreased ionization signal relative to the thermal signal will cause a background event which interacts at the surface to be misidentified as a signal event. We can use information about the shape of the thermal signal pulse to discriminate against these surface events. Using a subset of our calibration set which contains a large fraction of electron events, we can characterize the expected behavior of surface events and construct a cut to remove them from our candidate signal events. ...
T. Saab, Search for Weakly Interacting Massive Particles with the Cryogenic Dark Matter Search Experiment, Ph.D. Thesis, Stanford University
T.A. Perera, The Limiting Background in a Dark Matter Search at Shallow Depth, Ph.D. Thesis, Department of Physics, Case Western Reserve University
The first phase of the experiment, conducted at a shallow site, is limited by a background of neutrons which are indistinguishable from WIMPs in terms of the acquired data. By accounting for and statistically subtracting these neutrons, CDMS I provides the best dark matter limits to date over a wide range of WIMP masses above 10 GeV/c2. These results also exclude the signal region claimed by the DAMA annual modulation search at a >71% confidence level.
The second phase of the experiment, located at a deep site, is scheduled to begin data acquisition in 2002. Due to longer exposures, larger detector mass, and low background rates at this site, data from CDMS II are expected to improve on present WIMP sensitivity by about two orders of magnitude....
S. Golwala, Exclusion Limits on WIMP-Nucleon Elastic Scattering Cross-Section from the Cryogenic Dark Matter Search, Ph.D. Thesis, Department of Physics, University of California, Berkeley
The Cryogenic Dark Matter Search (CDMS) employs Ge and Si detectors to search for WIMPs via their elastic-scatteringin teractions with nuclei while discriminating against interactions of background particles. The former yield nuclear recoils while the latter produce electron recoils. The ionization yield (the ratio of ionization production to recoil energy in a semiconductor) of a particle interaction differs greatly for nuclear and electron recoils. CDMS detectors measure phonon and electron-hole-pair production to determine recoil energy and ionization yield for each event and thereby discriminate nuclear recoils from electron recoils.
This dissertation reports new limits on the spin-independentWIMP-nucleon elastic-scattering cross section that exclude unexplored parameter space above 10 GeV c-2 WIMP mass and, at > 75% CL, the entire 3s allowed region for the WIMP signal reported by the DAMA experiment. The experimental apparatus, detector performance, and data analysis are fully described.
A.H. Sonnenschein, A Search for Weakly Interacting Dark Matter Particles with Low Temperature Detectors Capable of Simultaneously Measuring Ionization and Heat, Ph.D. Thesis, Department of Physics, University of California at Santa Barbara
R. Clarke, An Athermal Phonon Mediated Dark Matter Detector With Surface Event Discrimination, Ph.D. Thesis, Department of Physics, Stanford University
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S. Nam, Development of Phonon-Mediated Cryogenic Particle Detectors with Electron and Nuclear Recoil Discrimination, Ph.D. Thesis, Department of Physics, Stanford University
This thesis describes the development of silicon based cryogenic particle detectors designed to directly detect interactions with these WIMPs. These detectors are part of a new class of detectors which are able to reject background events by simultaneously measuring energy deposited into phonons versus electron hole pairs. By using the phonon sensors with the ionization sensors to compare the partitioning of energy between phonons and ionizations we can discriminate betweeen electron recoil events (background radiation) and nuclear recoil events (dark matter events). These detectors with built-in background rejection are a major advance in background rejection over previous searches.
Much of this thesis will describe work in scaling the detectors from 1/4 g prototype devices to a fully functional prototype 100 g dark matter detector. In particular, many sensors were fabricated and tested to understand the behavior of our phonon sensors, Quasipartice trapping assisted Electrothermal feedback Transition edge sensors (QETs). The QET sensors utilize aluminum quasiparticle traps attached to tungsten superconducting transition edge sensors patterned on a silicon substrate. The tungsten lines are voltage biased and self-regulate in the transition region. Phonons from particle interations within the silicon propogate to the surface where they are absorbed by the aluminum generating quasiparticles in the aluminum. The quasiparticles diffuse into the tungsten and couple energy into the tungsten electron system. Consequently, the tungsten increases in resistance and causes a current pulse which is measured with a high bandwidth SQUID system....
P. D. Barnes, Jr., The Cryogenic Dark Matter Search (CDMS), Ph.D. Thesis, Department of Physics, University of California, Berkeley
We would like to measure the properties of the dark matter directly. Supposing that the dark matter consists of a new fundamental particle, a WIMP, that was in thermal equilibrium in the early universe, we have built an experiment to detect dark matter directly by elastic scattering with germanium or silicon nuclei. Our detectors are large (~ 200 g) calorimeters that can discriminate between interactions with the electrons, due to background photons and beta particles, and interactions with the nuclei, due to WIMPs and background neutrons. The detectors operate at low temperatures (~ 20 mK) in a specially constructed cryostat. To reduce the rate of background events to a manageable level, the detectors and cryostat have been constructed out of selected materials and properly shielded. This dissertation discusses the properties of the hypothetical WIMPs, the detectors, cryostat, and shielding system, and finally, the analysis methods.
A.J. Da Silva, Development of a Low Background Environment for the Cryogenic Dark Matter Search, Ph.D. Thesis, Department of Physics, University British Columbia
Direct detection experiments look for nuclear recoils from WIMPs scattering in a detector. The first generation of direct detection experiments were ultimately limited by radioactive backgrounds. The Cryogenic Dark Matter Search (CDMS) is a direct detection experiment based on novel particle detectors operated at millikelvin temperatures that provide intrinsic background rejection. This capability, however, is not 100% effective. Therefore a low background environment is essential to the experiment.
To create such an environment, all possible background sources have been extensively studied both by measuring the background contribution from muons, phonons and neutrons and by performing detailed Monte Carlo simulations of the photon and neutron backgrounds. The results of this investigation, as discussed in this thesis, have influenced all aspects of the CDMS experiment....
W.K. Stockwell, "A Cryogenic Search for WIMP Dark Matter," Ph.D. Thesis, Department of Physics, University of California, Berkeley
K.D. Irwin, Phonon-Mediated Particle Detection Using Superconducting Tungsten Transition-Edge Sensors, Ph.D. Thesis, Department of Physics, Stanford University
The detectors described here consist of a tungsten thin film deposited on a silicon substrate. When an incident particle scatters in the silicon crystal, it deposits energy in the form of phonons which propagate to the surface of the crystal where they are absorbed in the tungsten thin film. The superconducting film is biased at or near its transition temperature. Changes in the resistance of the film are measured.
The superconducting titanium transition-edge sensors previously developed by our group exhibit a threshold phonon energy density below which no signal is detectable. This threshold density poses severe restrictions on resolution, energy threshold, and absorber mass. In order to overcome these limitations, several new technologies were developed. In each case, a superconducting film with a sharp transition well below that of titanium (~ 380 mK) is necessary. To this end superconducting W films were developed with ~ 1 mK wide transitions at 70 mK. Before this work W thin films always exhibited transition temperatures > 600 mK....
M. Penn, Nuclear-Recoil/Electron-Recoil Discrimination In Cryogenic Silicon Detectors For Use In Dark Matter Searches, Ph.D. Thesis, Department of Physics, Stanford University
The physics of charge measurement, necessary for the background rejection technique, in silicon at low temperature (T < 0.5 K) and low applied electric field (E = 0.1 - 100 V/cm) has been examined in a variety of high purity, p-type silicon samples with room temperature resistivity in the range 2 - 40 kΩ-cm. The samples varied in thickness from 300 μm to nearly 5 mm. Charge loss at low electric field due to trapping during charge drift is present but the data suggest that another charge-loss mechanism is also important. We present results which indicate that a significant fraction of the total charge loss (compared to full collection) occurs in the initial charge cloud near the event location. A simple model of charge trapping both in the initial cloud and along the electric field induced drift to the electrodes is developed and satisfactory comparison to the data is found. In addition, measurements of the lateral size, transverse to the applied electric field, of the initial electron-hole cloud indicate large transverse diffusion lengths. At the lowest fields a lateral diameter on the order of 1 mm is found in samples ~ 5 mm thick.
T. A. Shutt, A Dark Matter Detector Based on the Simultaneous Measurement of Phonons and Ionization at 20 mK, Ph.D. Thesis, Department of Physics, University of California, Berkeley
We have developed a novel particle detector to look for dark matter based on the simultaneous measurement of ionization and phonons in a 60 g crystal of high purity germanium at a temperature of 20 mK. Background events can be distinguished by our detector because they produce more ionization per unit phonon energy than dark matter interactions.
The phonon energy is measured as a temperature change in the detector by means of neutron transmutation doped germanium thermistors attached to they crystal. The ionization measurement is accomplished by applying a bias to implanted contacts on the faces of the disk. Charge collection differs from the normal situation at 77 K in efficiency is good with an electric field of only ~0.2 V/cm after the charged impurities in the crystal have been neutralized by free charge created by particle interactions from a radioactive source. For fields below this charge collection is poor, and affects the amount of phonon energy measured. We have modeled this in terms of charge trapping.
N. Wang, "A Cryogenic Phonon Detector to Search for Dark Matter Particles," Ph.D. Thesis, Department of Physics, University of California, Berkeley (not available in electronic format)