Imaging and Spectral Performance of a 60 $\mu$m Pitch CdTe Double-Sided Strip Detector

The CdTe-DSD provides two independent measurements of energy from its anode and cathode electrodes. Figure 2 shows two ²⁴¹Am spectra obtained by the two sides of the detector. The detector was irradiated on the cathode side. If energy is detected on two or more adjacent strips (multi-strip event), the total sum of energies on the adjacent strips are used. In the anode side spectrum, energy resolutions are 1.1 keV at 14 keV and 1.4 keV at 60 keV in FWHM. Below 20 keV, the cathode side spectrum is almost identical to that of the anode side. In contrast, the peaks above 20 keV exhibit low-energy tails. This tail structure is caused by the depth dependence of the induced charge due to the charge trapping effect[takahashi2001recent, salcin2014, He2001].

When high energy photons ($>$20 keV) enter the detector, some of the photons penetrate relatively deeply into the detector and the depth of interaction (DoI) is a vertically spread distribution. As the DoI becomes deeper, the total measured energy on the cathode electrodes gets smaller, creating a tail on the peak toward low energies. Figure 3 compares the energies measured by the cathode and anode sides. The low-energy tail on the 60 keV cathode-side peak is indicated by the red region. For low energies ($<$20 keV), the anode and cathode energy spectra are almost identical and averaging both measurements results in the expected energy resolution improvement[Watanabecdte2009]. However, for higher energies ($>$20 keV), a more complicated correction is required to improve the energy resolution. We have applied an algorithm applicable up to at least 60 keV, confirming the spectroscopic performance improvement across the entire range.

When the anode side energy and the cathode side energy are equal within a certain margin, a simple average works well to obtain a superior energy resolution. Figure 4 shows the averaged spectrum when the difference between the anode and cathode side energy is within the energy resolution. The energy resolution at 14 keV is 1.1 keV(FWHM) or 0.47 keV($\sigma$) in both the anode and cathode spectra. The 1$\sigma$ resolution of the energy difference ($E_{Pt}-E_{Al}$) is 0.66 keV. In this paper we define $\pm 1.5\sigma$ of the combined energy as the margin in which simple averaging is utilized.

Below 23 keV, most of the events fall in this margin shown by the blue region in Figure. 3. If the energy resolution is dominated an effect of the readout electronics on each side, the energy resolution will improve by $1/\sqrt{2}$ by averaging the energies measured by the anode side and cathode side. The improved energy resolution of 0.76 keV in the averaged spectrum is highly consistent with this number.

However, when the difference is larger than the threshold, the same method is no longer useful and only results in a degradation of energy resolution. This is due to the tail structure shown in the red region in Figure. 3. At high energies, most events do not fall in the margin and it would degrade the lack of detection efficiency at high energy if we only use the events in the margin. To achieve the best possible energy resolution while mitigating the loss of events, this tail structure must be corrected.

To correct the tail structure, we define a tail angle $\theta$ as the angle between the horizontal axis and the tail structure axis. To calculate the angle, principle component analysis (PCA) is used and the tail structure axis is defined as the first principal component axis, i.e. the direction that maximizes the data variance along the axis (Figure 5(a)). For the actual analysis, we utilized the TPrincipal class in ROOT framework[brun1997]. To apply this framework, counts are distributed randomly in each bin of a 2-dimensional histogram of the energy average and difference of both sides and bins with less than three counts are ignored. We calculate the tail angle for every pixel, using principal component analysis, and make a distribution of the tail angle for all pixels (Figure 5(b)). The standard deviation is 1.2 degrees, which is approximately 2% of the peak value. From this result we assume theta is constant across pixels and independent of measured energy for a given branch on the plot, and is well represented by its peak value. By using the peak value of the tail angle $\theta_{d}=59.0^{\circ}$, we can reconstruct the correct energy.

The incident energy reconstruction algorithm used in this paper is as follows:
If the absolute energy difference between the anode and cathode energies is

• 1.

  within 1.0 keV:  $|E_{Pt}-E_{Al}|<1.0$ keV
  The reconstructed energy is equal to the average energy.

• 2.

  less than $-1.0$ keV:  $E_{Pt}-E_{Al}<-1.0$ keV
  The reconstruction function is the linear combination of the difference and the average of the energies, with the reconstructed energy contour line aligned parallel to the tail-like structure. Tail angles are calculated by PCA in each pixel of the detector. The peak of the distribution for all pixels is used as the representative value $\theta_{d}=59.0^{\circ}$.

• 3.

  greater than 1.0 keV:  $E_{Pt}-E_{Al}>1.0$ keV
  The tail angle $\theta_{u}$ is determined as 55.3^∘ by the PCA on the energy ”average vs difference” plot summed over the detector. It is assumed that the tail structure in this case is caused by the events which photons interact very close to the cathode side[salcin2014] and the percentage of this event is 5.3%.

By applying this method, the energy resolution of 60 keV peak is improved. In Figure 6, 60 keV peaks in the averaged spectrum (blue) and the spectrum obtained by the above method (red) with an energy difference greater than 1 keV are compared. The averaged spectrum with an energy difference within 1 keV (black) is also superimposed. While averaging fails to correct the tail structure, the method introduced in this section allows to mitigate the degradation of energy resolution even when the energy difference is large. By using this tail-corrected spectrum, the lack of efficiency at high energy is mitigated while keeping the energy resolution.

The energy of incident photons can be properly reconstructed by using the method discussed in the previous section. This makes it possible to accurately assess the energy dependence of charge shared events. Figure 7 shows the incident photon energy and the degree of charge sharing between adjacent strips. As the incident photon energy increases, the charge shared event increases for both sides. It is thought that since the initial charge cloud size is roughly proportional to the incident energy (due to electrostatic repulsion) the fraction of multiple events increases for higher energies. There is also the effect that multiple events are more likely to detect at high energies because the energy threshold of each strip is set at 1.5 keV

We examine the relationship between the depth of photon interaction and the ratio of charge shared events. It is to be noted that the difference between the cathode and anode side energy represents the depth of photon interaction. If photons interact near the surface of the anode side, more holes are trapped and a lower energy than expected is observed in the cathode side. Figure 8 represents the correlation of the energy difference (i.e. photon interaction depth) and ratio of charge shared events. As photons interact near the surface of the anode side, charge shared events at the cathode side increase. This indicates that the longer the charge takes to travel to the electrodes, the more likely it is that a charge shared event occurs.