E. Kalemci and J.L. Matteson
Center for Astrophysics and Space Sciences, University of California, San Diego
La Jolla, CA, 92093-0424

We have developed and tested position-sensitive cross-strip CZT detectors for use in X-ray astronomy in collaboration with Washington University in St. Louis. We have also developed a model of charge production and drift in the detectors and charge induction on the electrodes to better understand the properties of these detectors. The model accounts for the electric field in the detector, weighting potentials of the electrodes, trapping, photoelectron range, and diffusion of the resulting charge cloud. We describe the model and show its predictions of the size of drifting charge clouds in a CZT detector agree well with laboratory measurements.

CZT has desirable features for the detection of X-rays, e.g., high Z and density, compatibility with small electrodes for position readout, and high resistivity ~10¹¹ W -cm at 300 K due to its large band gap, ~1.54 eV. The latter property makes it a "room temperature semiconductor" and allows it to be operated at these temperatures with low leakage currents and good energy resolution [1]. CZT is well suited to important objectives of high-energy astronomy from ~10 to 100's of keV, e.g., a full sky monitor/survey at a sensitivity that will yield thousands of new sources, localizing gamma-ray bursts to a few arc minutes, and deep exposures to individual sources with focusing hard X-ray telescopes. HEXIS, FAR-XITE, CONSTELLATION X, MARGIE, and EXIST are proposed space and balloon missions utilizing position-sensitive CZT detectors. SWIFT, a space mission in development, employs an array of discrete CZT detectors.

Previously, we developed a model to predict the induced signal on each electrode as a function of time in a CZT strip detector for any interaction position [2]. This did not include diffusion and photoelectron range. Here we add these effects to the model and use them to understand charge sharing between the anodes. Kalemci and Matteson [3,4] provide a more complete description of this work.

We used the UCSD-WU prototype CZT detector [1], shown in Fig. 1, which has 22 anode and 22 orthogonal cathode strips. A set of steering electrodes is interlaced between the anodes to enhance charge collection. Anode and steering electrode widths are 100 m m, cathodes are 450 m m, and the pitch is 500†m m. Anodes are biased at 200 V and the steering electrode at†180 V. Radiation is incident on the cathode side and the anode signals are used for spectroscopy. Cathode signals allow interactions to be localized to a single anode-cathode intersection. The detector was manufactured from "discriminator grade" CZT by eV Products.

Below 250 keV most X-rays interact by the photoelectric effect and the ejected photoelectron creates electron-hole pairs along its path. The photoelectron range varies with energy as ~E^1.8 and is 47 m m at 100 keV. Such a photoelectron loses half its energy the last ~10 mm of its path, and thus its initial charge cloud has this scale. A K X-ray of ~25 keV (~170 m m mean free path) may be produced in the X-ray interaction. The electron and hole clouds drift to the electrodes along the electric field lines, shown in Fig. 2. The charges induce time-dependent signals on the electrodes, which are calculated with Ramo’s weighting potential technique [5]. Fig. 3 shows the weighting potentials. The model includes charge trapping, and trapped charges produce partial signals according to the weighting potentials at their positions. With fitted trapping lengths of 60 mm and 0.24 mm for electrons and holes, respectively, the predicted signals on electrodes versus interaction depth are shown in Fig. 4. Anode signals depend weakly on depth due to the large electron trapping length and compact weighting potential, which makes them quite insensitive to trapped holes. Cathode signals, however, decrease strongly with interaction depth since they are due to holes, many of which are trapped. When three neighboring cathodes' signals are summed, the depth dependence is nearly linear, as Fig. 4 shows. Measurements with flood illumination that show the model describes the temporal properties of charge induction, trapping, and total charge very well [2]. For example, the anode signal's depth dependence is predicted to be a function of the summed-cathode/anode ratio, and Fig. 5 shows excellent agreement, <1%, of the fitted model with measurements under flood illumination. We use the cathode/anode ratio to correct the peak broadening due to depth dependent anode signals at energies above ~80 keV [2].

Electrons diffuse while they drift, making the clouds larger. The lateral, or 1-dimensional, density profile can be found by the solution of Fick’s equation, and is given by [6]

M(x,t) = (M_o / (4 p D t)^1/2) Exp [-x² / 4 D t] (1)

where M is the concentration, x is the lateral position and t is the time, M_o is the initial concentration, and D is the Einstein coefficient, ~26†cm²/s, which corresponds to an electron mobility of 1000 cm²/V-s. Since the drift time to the anodes increases as interactions become shallower, the size of the electron clouds at the anodes is greatest for interactions near the cathodes. In this case, the electron cloud will diffuse to a radius of ~80 mm [3,4].

Charge sharing: measurements and results

Recently, we made direct studies of the effects of diffusion and photoelectron range. To have a precise knowledge of interaction sites' positions, we used our 30 mm collimated beam [7] of 122 keV radiation from ⁵⁷Co. We scanned the beam perpendicular to the anodes and studied the pulse height distributions of the anode signals.

Scatter plots of signals on two neighbor anodes summarize the results (Fig. 6) and show the signals are a strong function of beam position. At Position: +250 m m, directly over the center of Anode 2, all the signal is collected by Anode 2 and the 122 keV peak can be seen at channel 102. As the beam is moved toward Anode 1 (smaller position values) an increasing fraction of the events produce signal on both anodes, i.e., their charge is shared by the anodes. At a Position: 0 m m, directly over the steering electrode, all events are shared. The points on or near the diagonal line (x + y = 122 keV) produce full signal, albeit with energy resolution that is degraded by 2^1/2, since two electronic channels' noise is present. Shared signals may result from propagation of K X-rays to the next anode's charge collection region. These are not true charge sharing events and can be recognized by their discrete energy, ~25 keV, being deposited at one anode, e.g., lower right panel of Fig. 6. Such events were excluded for the analysis described below.

We attribute charge sharing to diffusion and photoelectron range. They cause the electron clouds to become so large their lateral extent may be beyond the steering electrode and thus reach the detector volume with charge collection onto the neighboring anode. First, we consider diffusion qualitatively. We expect sharing to be greater for interactions near the cathode, since diffusion will give these events larger charge clouds at the anodes due to their longer drift times. We show this to be the case by comparing the sharing effects for interactions near the top (cathodes) and the bottom of the detector, both for a beam position of 40 mm (from the steering electrode center). Events' depths were inferred from their cathode-to-anode signal ratio [2]; deeper events have smaller ratios. Results are shown in Fig. 7. The left panel is for the top 0.2 mm of the detector and charge sharing occurs in most events, i.e., signals mostly occur on both anodes. However, most interactions near the bottom (1.4 - 1.6 mm depth, right panel) were fully collected at Anode 1, i.e., there is little sharing.

Next, we describe a quantitative assessment of charge sharing's dependence on depth of interaction, comparing model predictions with measurements. We defined the onset of sharing for each depth as the beam position at which the neighbor anode first received more than 5% of the signal for at least 5% of the events. This was predicted by integrating eq. (1) to find x where 5% of the cloud lies beyond x, and combining this with the beam dispersion and photoelectron trajectories. Experimentally, onset was recognized in a series of Anode1/Anode2 scatter plots, like Fig. 4, for 20 mm steps in beam position. Since the positions were discrete, the true onset positions were bounded by the measurement positions.

Results are shown in Table 1. At each depth, 41†mm of the predicted onset position is due to photoelectron range, 20 mm to the radius of the collimated beam (broadened by transmission at the edges), and the remainder to diffusion. Uncertainties in the predictions are due to approximations used for the distribution of interactions versus depth, K X-ray effects, and the assumption that the initial electron cloud is a delta-function at a range-weighted position. Uncertainties in the measurements are due to the position readout precision. A slight tilt of the beam from perpendicularity was taken into account, resulting in observed values that are not integer factors of 20 m m, allowing tighter limits to be placed at 0.1 mm average depth. For all depths, the results show the predicted onset is within the bounds provided by the measured values, quantitatively confirming our detector model. It is significant that both diffusion and photoelectron range must be included in the predicted values to have agreement with the measurements.