SUPERCDMS SOUDAN OVERVIEW
2.2.5 Ionization Signal
(a) Electron Transport (b) Hole Transport
Figure 2.12: Simulation of charge transport in an iZIP from [47]. Left (a): electron propagation simulation in Ge. Due to the indirect nature of the Ge band gap the electrons propagate along four channels aligned along the [111], [¯111], [1¯11], and [¯1¯11] lattice directions. Right (b): hole propagation simulation.
main in the channel they initially propagated into. From simulation, these channels were measured to be≈33◦from vertical as can be seen in figure 2.12. The holes are much simpler and propagate as if they have an effective mass that is a scalar, and any spreading in the XY direction is due to random scattering. This causes the ef- fective spot size of the collected charge carriers to be quite different on the electron collecting face, and hole collecting face. This has important implications for po- sition reconstruction (see section 2.4.4), and can also cause incomplete ionization signal collection due to surface trapping.
Surface Trapping
The simplified model of a our Ge semiconductor, with its valence and conduction band separated by a clean band gap, is fairly accurate in the bulk of the crystal, but begins to break down near the surfaces of the detector. The concern is that inter- actions near the surface of the detector could suffer from incomplete collection of the ionization signal for an interaction, which substantially confuses our ability to differentiate between signal and background on an event-by-event basis. Qualita- tively, we approach this phenomena from two angles, one for interactions occurring near the flat top and bottom surface of the detector (called the detector “faces”) and the other for interactions near the vertical cylindrical portion of the detector (called the detector “sidewall”).
Figure 2.13: Ionization collection for three different classes of particle interactions.
A bulk interaction is expected to undergo symmetric collection of electrons and holes. Any near-face interactions however will preferentially be collected on the same side, allowing for an ionization-based Z-position proxy to be constructed [44].
For interactions very near26 the faces of our detectors a portion of the electron- hole cloud will diffuse directly into the ionization collecting electrode27, and will suppress the ionization signal by up to 30%. This can be mitigated to some degree by electrically isolating the ionization electrodes from the crystal substrate. This was a large problem for the oZIP detectors used in CDMS II, and the impetus for the new interleaved design of the iZIP detector [34]. During normal operation, the ionization electrodes are biased to±2 V, and the phonon lines are grounded. This creates a uniform drift field in the volume, but near the faces the field is tangential to the detector surface and much higher in strength. This can be seen in figure 2.13.
Due to this field configuration only interactions occurring in the bulk of the crystal will induce ionization signals on both faces of the detector; those near the faces will see the electrons and holes collected on a single face. This allows analyzers to selectively exclude near-face events.
Interactions near the sidewall are also problematic. As this is a physical boundary,
26On the order of a few microns [48].
27A process referred to as “back diffusion”
the lattice is unable to repeat regularly. Even if the surface were perfectly smooth, regular, and pure, the Ge itself would have many dangling bonds that could poten- tially trap electrons and holes and prevent their collection. In reality the surface is rough and amorphous, allowing for many energy levels in what would otherwise be the band gap. These local potential energy wells can easily acts as traps at the low drift-fields used in our detectors. The oblique propagation exhibited by electrons makes the ionization signal collected on the top (electron-collecting) face especially susceptible to under-collection. This effect is dependent on the interaction location, and is addressed in analysis in a number of ways. First, when estimating the total ionization energy of the interaction, only the face that collects more ionization is used or
EIonizationtotal = max{EelectronIonization,EholeIonization} (2.7) Within the CDMS Analysis Package28 (CAP) this total ionization energy estimate is spelledqsummaxOF. Second, the ionization collectors for each face are arranged into an inner disk collector surrounded by an outer annular electrode. This allow us to construct a proxy for the radial position of an interaction by examining the partitioning of signal between these two detectors. This technique is of central importance to this analysis and covered in much more detail in section 2.4.4.
Bulk trapping/neutralization
Although the very surface of the detector is always a problem from a charge col- lection standpoint the charge carriers may also run into propagation problems in the bulk of the crystal. Any impurity, or lattice defect may act as a scattering site, and at very low temperatures and bias voltages electrons and holes can be trapped at such sites as can be seen in figure 2.14. As holes are drifted downward toward the negatively biased face and electrons towards the positive bias, over time this trapping will produce a continuous space charge distribution that canceles the drift field, severely impacting the ionization signal. There are a few methods that are used to neutralize this space charge and, although the details depend on the operat- ing mode of the detector in question, in general they involve grounding both faces of the detector and then producing many charge carriers in the detector. These will neutralize the space charge.
28A custom MATLAB-based analysis environment.
Figure 2.14: Collection efficiency vs bias voltage (Vb). At higher bias voltages most charge carriers can overcome any local traps, and the collection efficiency is quite high. This regime produces excessive Luke phonons however, and the optimal balance between the two effects was chosen at±2 V [44].
During WIMP-search operation, event rates are low enough that the timescale of space-charge buildup is on the order of hours. As a result our WIMP-search data is taken in time-blocks or “series” of three hours, and between each series our de- tectors are neutralized via a process referred to as “flashing”. Each of our iZIP detectors is instrumented with 4 LEDs installed on the readout DIBs near its sur- face, which are briefly illuminated while the detectors are grounded between series.
Although these photons only excite electron-hole pairs in the outer ∼1 mm of the crystal, the field from the space charge itself will, in the absence of a bias voltage, allow the detector to be neutralized. After neutralization, the detectors are re-cooled and the next series of data-taking may be started.
Event rates during calibration are much higher, and as a result it takes tens of min- utes, rather than hours, for space-charge buildup to become a problem. This is the same timescale as a post-flash cool-down. In an effort to keep our data-taking duty factor above 50%, we can actually exploit the high event rate from calibration as our source of neutralizing charge-carriers. During calibration, neutralization simply requires briefly grounding voltage bias lines.
There is another source of space charge that requires special attention. During the initial cooling (or re-cooling) of our detector from high temperatures, many charge carriers from the conduction band will relax into meta-stable traps in the band gap (levels that are again caused by impurities, vacancies or lattice abnormalities). Un- like the space charge distribution that arises during normal detector operation, how- ever, the trapped electrons and holes will be randomly positioned in the detector.
Figure 2.15: Transimpedance amplifier readout circuit for our iZIP’s ionization collection lines [49].
As a result they will not induce the large scale drift field which typically aids neu- tralization, requiring an extended flashing procedure.