SUPERCDMS SOUDAN OVERVIEW
2.4.4 Ionization Based Position Estimation
As mentioned in section 2.2.5 our new iZIP detectors have a few improvements over the CDMS II oZIP-style detector. First, the ionization- and phonon-collecting lines are interdigitated, with the ionization lines biased at±2 V and the phonon lines held at ground. This creates a uniform drift field in the bulk of the crystal and a highly tangential field near the face. The second major difference is that both faces are symmetrically instrumented.
Ionization Z position
In an oZIP style detector, interactions that happen within∼10µm of a detector face run into a couple of problems. First, there is a layer of amorphous Ge near the face that has an entirely different band structure than the bulk of the crystalline Ge. It is
possible to trap charge in this amorphous layer, leading to reduced collection. Sec- ond, the when they are initially produced, the charge carries are quite hot and until they relax down to near the conduction ground state their movement is dominated by thermal diffusion, rather than the drift field. As a result, these charge carriers can directly diffuse into the phonon collection circuits (which would produce no ioniza- tion signal) or even into the wrong ionization collector (potentially canceling actual signal). It is something akin to this “wrong side collection” behavior that iZIPs were specifically designed to exploit. In an iZIP, an interaction in the bulk will lead to symmetric collection of electrons and holes. An interaction within∼1 mm of ei- ther face, however, will encounter the transverse field as seen in figure 2.13. In this case charge carriers will not cross the crystal but instead be collected entirely on a single face36. As both faces of an iZIP are instrumented to collect charge, we can use this information to construct an ionization-based, Z-position estimateZIonization from ionization collection:
ZIonization = EelectronIonization−EholeIonization
EelectronIonization+EholeIonization (2.22) WhereE{electron,Ionizationhole}is the energy estimate from the collection of electrons or holes respectively. This parameter varies from −1 (a hole-collection-side surface event interaction) to 1 (an electron-collection-side surface event interaction) with 0 being a bulk interaction. In practice, a uniformly illuminated detector will form three clus- tered distributions around these values of−1, 0, and 1 as seen in figure 2.23. In CAP, ZIonizationis spelledpzpartOF. As near-face surface event identification was a major design goal of our iZIP detectors, two210Pb sources were installed in situ to produce a controlled near-face surface event population for more detailed study. One was situated above the top face of detector iT3Z1 to produce electron-collection surface events while the other was situated below the bottom face or detector iT3Z3 for the creation of the equivalent hole-collection surface events. The first∼900 live-hours of our Soudan dataset were used to study our ability to identify these near-face sur- face events the results of which can be seen in figure 2.24. In an attempt to only study the effects of near-face surface events, as opposed to near-sidewall surface events, this study was restricted to interactions in which the ionization signal was completely collected by the inner electrode. This effectively reduced the detector mass to∼30% of its of its value. If we wish for the best possible sensitivity we need
36With the “wrong side” charge carriers being collected on the grounded electrodes and thus not sensed at all.
Figure 2.23: Plot of ionization z partition vs. recoil energy for a set of 252Cf- sourced calibration events in detector IT1Z1. Example fiducializing cuts (which are very similar to those used in our “preselection region”) are shown dividing surface events (red) from bulk events (blue).
to have a look at radial position in more detail as well.
Ionization radial position
As with near-face surface events, near-sidewall surface events may experience charge trapping if the drifted charge carriers encounter the sidewall. Unlike with near-face surface events, however, this phenomena may extend to interactions happening may millimeters away from any surface of the detector. This is especially pronounced when examining the ionization signal from electron collection. Due to the oblique propagation discussed in section 2.2.5, events occurring deep in the detector and far away from the electron-collecting face are epically susceptible. This effect may be mitigated by calculating the total number of charge-carriers created and the as- sociated ionization energy estimate, EIonization, by simply calculating the ionization energy separately for the electron and hole collecting sensors and taking the maxi- mum as was seen in equation 2.7. In CAP, this representation ofEIonization is spelled qsummaxOF. This estimate has the benefit of automatically discarding an ioniza-
tion signal that is under-collected. This is helpful for interactions occurring near each of the faces, but runs into difficulty for high-radius events, where both elec- tron and holes could be trapped. It is useful to then define an R-position estimate, RIonization{electron,hole}
RIonization{electron,hole} = EIonization Outer {electron,hole}
E{electron,hole}Ionization
(2.23) whereEIonization Outer
{electron,hole} is the ionization energy collected in the annular guard-ring elec- trode. The ionization R position estimate varies from 0 for an interaction in the bulk of the detector, to 1 for a high-radius event as can be seen in figure 2.25. Unlike with our ionization Z position estimate, there are two basic estimates to choose from, one from the electron signal and one from the holes. Each of these two estimates will be more or less reliable depending on the vertical interaction location. From a very abstract standpoint, this is not a problem. Any multidimensional machine-learning technique should be able learn which of these position estimates is more reliable based on all other available information. In practice, however, a single reliable ra- dial position is vital for the exploratory phase of an analysis of this type. If human analyzers are going to want to remove the obviously very-high-radius events by hand, or better yet preform any sort of cross-check on the final analysis result, it is important that we have a good physical understanding of the variable we are cutting on.
A naive approach to construct a combined ionization radial position estimate would be to follow in the footsteps of our EIonization definition and simply rely on the ion- ization radial position estimate from the face that collected more energy as in:
RIonization =
RIonizationelectron , ZIonization ≥0 RIonizationhole , ZIonization <0
(2.24)
The problem with this definition is that for the majority of the interior volume of the detector, the charge collection on both faces will be essentially symmetric, but the value ofZIonization will fluctuate slightly negative or positive due to noise. This will lead to potentially throwing away the more accurate radial estimator. An improve- ment would be to use pure electron or hole information only for events that are truly single-side collection, and a linear combination both electron and hole information
collection symmetrically. The definition that was settled on used the more tightly collimated hole collection side for every event where more holes are collected than electrons, and only utilizes this linear combination for events with an excess of electrons.
RIonization =
RIonizationelectron , ZIonization > 1
RIonizationhole , ZIonization < 0
ZIonizationRIonizationelectron +(1−ZIonization)RIonizationhole , otherwise
(2.26)
As a final check to ensure a sensible, physically well motivated definition for radial position we turned to our on-going Detector Monte-Carlo (DMC) effort. Although not considered “production ready” at the time of this analysis, most of the known DMC discrepancies arise from difficulties simulating the phonon rather than ion- ization signal path, which is the more mature of the two. I have made a number of plots in figure 2.26 depicting how each of the above positions estimates maps to real physical interaction locations. In CAPRionizationis spelledqrpartOF_zhalf.