Invited Review Article: Physics and Monte Carlo techniques as relevant to cryogenic, phonon, and ionization readout of Cryogenic Dark Matter Search radiation detectors

Abstract

This review discusses detector physics and Monte Carlo techniques for cryogenic, radiation detectors that utilize combined phonon and ionization readout. A general review of cryogenic phonon and charge transport is provided along with specific details of the Cryogenic Dark Matter Search detector instrumentation. In particular this review covers quasidiffusive phonon transport, which includes phonon focusing, anharmonic decay and isotope scattering. The interaction of phonons in the detector surface is discussed along with the downconversion of phonons in superconducting films. The charge transport physics include a mass tensor which results from the crystal band structure and is modeled with a Herring Vogt transformation. Charge scattering processes involve the creation of Neganov-Luke phonons. Transition-edge-sensor (TES) simulations include a full electric circuit description and all thermal processes including Joule heating, cooling to the substrate and thermal diffusion within the TES, the latter of which is necessary to model normal-superconducting phase separation. Relevant numerical constants are provided for these physical processes in germanium, silicon, aluminum and tungsten. Random number sampling methods including inverse cumulative distribution function (CDF) and rejection techniques are reviewed. To improve the efficiency of charge transport modeling, an additional second order inverse CDF method is developed here along with an efficient barycentric coordinate sampling method of electric fields. Results are provided in a manner that is convenient for use in Monte Carlo and references are provided for validation of these models. Contents

Optimizing the design and analysis of cryogenic semiconductor dark matter detectors for maximum sensitivity

“…As described by Steve [90] and Daniel [4] but also by a plethora of more primary documents ( [20],. .…”

“…The primary reason is that, as of this writing, the detector monte carlo is not quite to the development stage where reproduction of physical phonon and charge signals has been shown to be physically consistent with experiment (but it is really close!). Secondly, even if this was possible currently, my thesis would only briefly discuss these issues, because I stopped personally contributing to the monte carlo effort 4 years ago and thus under the spirit of complementarity of theses, a reader would be much better served by reading about these efforts and successes in Kevin McCarthy's soon to be written thesis and in papers by Steve Leman [90] and Daniel Brandt [4].…”

“…This process also quite efficiently mixes the three different polarization states ( [90], [91], [92]), and consequently we can determine the polarization probabilities for a diffusing phonon by using the statistical mechanics principle that all quantum states which satisfy the interaction conservation rules (in this case energy conservation) are equally likely to be populated. Specifically, in the non-dispersive phonon limit where…”

“…(Right) Distribution of quasi particle energies after a p → qq interaction. Created by Paul [19] leakage issue [90]). Of course, the amount and frequency of phonon leakage depends significantly on the reflectivity of the Ge/Al interface and the Al film quality, either of which could significantly increase the average amount of time a phonon spends in the Al and thus could significantly decrease ν leak .…”

Advancing the Search for Dark Matter: from CDMS II to SuperCDMS

“…Luke phonons are emitted with low energies and correspondingly ballistic free paths, whereas the majority of Neganov-Luke phonons are produced in the strong near-surface fields at higher frequencies (-300 GHz and -700 GHz for electrons and holes) with correspondingly short mean free paths (-1.8 cm and -600 pm) [108,75] and fast absorption rates.…”