Fisher information analysis of depth-of-interaction estimation in double-sided strip detectors

Electron and holes, produced by the absorption of a gamma-ray photon in the depletion region of a semiconductor detector, drift towards their respective electrodes under the influence of the electric field created by a bias potential difference applied between the contacts. Carrier transport has an important impact on the signals observed with compound semiconductors such as CdTe and CdZnTe, as these materials are known to suffer from non-negligible trapping effects. Trapping causes the carrier-induced charge on the anodes and cathodes to become a function of where the electrons and holes are generated via the gamma-ray interaction in the crystal. The mean drift length of the charge carriers, and thus the significance of the effects of trapping, can be at least partially controlled by changing the magnitude of the applied bias voltage. Selection of operating bias voltage can therefore provide us a means to tune the sensitivity to gamma-ray depth-of-interaction (DOI). In very-high-resolution gamma-ray imaging applications, such as preclinical PET and SPECT, estimation of a 3D interaction location inside the detector crystal can be used to minimize parallax error in the imaging system. In this work, we investigate the effect of bias voltage setting on DOI estimates for a semiconductor detector with a double-sided strip geometry. We first examine the statistical properties of the signals and develop expressions for likelihoods for given gamma-ray interaction positions. Trapping effects are modeled as non-stationary spatial point processes. We use Fisher Information to quantify how well (in terms of variance) the measured signals can be used for DOI estimation with different bias-voltage settings. We performed measurements of detector response versus 3D position as a function of applied bias voltage by scanning with highly collimated synchrotron radiation at the Advanced Photon Source at Argonne National Laboratory. Experimental and theoretical results show that the optimum bias setting depends on whether or not the estimated event position will include the depth of interaction. We also found that for this detector geometry, the Fisher Information changes with depth.