Depth Calibration of Double-sided Strip Germanium Detectors for the Compton Spectrometer and Imager Satellite

TL;DR

This work addresses 3D position reconstruction in double-sided strip germanium detectors for a compact MeV gamma-ray telescope. It develops a depth calibration method by mapping the charge collection time difference $\tau_{\textrm{CTD}}$ to interaction depth $z$ using Julia-based SolidStateDetectors.jl simulations, validated against flood-source data from $^{241}$Am and $^{57}$Co. A per-pixel calibration is performed, yielding depth resolutions on the order of $\Delta z\approx0.8\text{ mm}$ at 59.5 keV and $\Delta z\approx0.5\text{ mm}$ at 122.1 keV for most pixels, with over 90% meeting sub-millimeter targets. The results demonstrate a practical, pixel-level approach to 3D position reconstruction in the COSI GeDs, enabling improved Compton event reconstruction and MeV imaging, while highlighting energy-dependent timing behavior and calibration nuances that warrant further study.

Abstract

Double-sided strip high-purity germanium detectors with three-dimensional position reconstruction capability have been developed over three decades, with space-based applications in high-energy astrophysics and heliophysics. Position resolution in three dimensions is key to reconstruction of Compton scattering events, including for the upcoming Compton Spectrometer and Imager (COSI) satellite mission. Two-dimensional position reconstruction is enabled by segmentation of the two detector faces into orthogonal strip contacts, enabling a pixelized analysis. The depth of an interaction cannot be measured directly but must be inferred from the charge collection time difference between the two faces of the detector. Here, we demonstrate for the first time the depth calibration of a detector with the COSI satellite geometry read out using an application specific integrated circuit (ASIC) developed for the COSI mission. In this work, we map collection time difference to depth using the Julia-based simulation package SolidStateDetectors$.$jl and validate it with comparison to the timing distributions observed in data. We also use simulations and data to demonstrate the depth resolution on a per-pixel basis, with >90% of pixels having <0.9 mm (FWHM) resolution at 59.5 keV and <0.6 mm (FWHM) resolution at 122.1 keV.

Figures (8)

• Figure 1: A 64-strip GeD in an engineering-model aluminum holder. The interposer board and connectors at the top of the image carry signal from the 64 HV strip contacts (visible and oriented vertically in this image), while the connectors on the left carry signal from the 64 LV strip contacts (hidden, and oriented horizontally). The guard ring contact encloses the 64 strip contacts on each face.
• Figure 2: $\tau_{\textrm{CTD}}$ distributions for an example pixel in HP52301-1 are shown for events in the $59.5\,\mathrm{keV}$ line of $^{241}$Am (a; $3\,\mathrm{ns}$ bin width) and the $122.1\,\mathrm{keV}$ line of $^{57}$Co (b; $8\,\mathrm{ns}$ bin width). For each source, data was collected with the source illuminating the GeD from the LV face (orange, peaked at $\tau_{\textrm{CTD}}$$\sim-160\,\mathrm{ns}$) and HV face (blue, peaked a $\tau_{\textrm{CTD}}$$\sim180\,\mathrm{ns}$).
• Figure 3: Simulated waveforms on the HV (red) and LV (black) contacts resulting from a charge cloud generated at $z = +4.6\,\mathrm{mm}$ in the detector and centered laterally on the example pixel. For both contacts, simulated pulses are illustrated after processing through the preamplifier (solid) and fast shaper (dashed). The dotted vertical lines indicate $\tau_p$, the start time for the TAC clocks at the peak of the shaped signal. $\tau_{\textrm{CTD}}$ is calculated according to \ref{['eq:CTD']} at $120\,\mathrm{ns}$.
• Figure 4: The simulated relation between charge collection time difference ($\tau_{\textrm{CTD}}$; defined in \ref{['eq:CTD']}) and interaction depth ($z$) is illustrated in blue. The HV face is at $z = +7.6\,\mathrm{mm}$. The waveform illustrated in \ref{['fig:waveforms']} constitutes a single point (indicated by the star) on this curve. The depth resolution ($\Delta z$) is calculated at depth $z$ by mapping $z$ to $\tau_{\textrm{CTD}}$ (black dotted line), adding the $\tau_{\textrm{CTD}}$ resolution (gray band) and mapping the band back onto depth.
• Figure 5: Fitted $\tau_{\textrm{CTD}}$ distributions for a single pixel illuminated with $^{241}$Am (upper) and $^{57}$Co (lower) from the LV (left) and HV (right) faces. The $^{57}$Co and $^{241}$Am fits were performed independently, but resulted in consistent fitted values for the stretch and offset. For each source, distributions from the two source positions were fitted jointly, with only $\Delta$$\tau_{\textrm{CTD}}$ allowed to vary between the LV- and HV-illuminated data. Residuals are reported based on the most probable number of counts in a bin according to the model.