A modeling method to calibrate the interaction depth in 3-D position sensitive CdZnTe gamma-ray spectrometers

The gamma ray interaction depth in 3-D position sensitive CdZnTe detectors is currently determined by the pulse height ratio of the cathode signal to the anode pixel signal (C/A ratio). In experiments with our 3-D CdZnTe detectors, the photopeak area as a function of the C/A ratio deviates from the expected exponential attenuation with depth. This indicates that the C/A ratio is not proportional to the true interaction depth. This paper proposes a method to calibrate the measured C/A ratio to the interaction depth by modeling the signals from the cathode and anode pixels. Knowing the detector's mobility-lifetime products of the electrons and holes from measurements, the expected pulse heights of the signals from the cathode and anode pixels can be calculated for different interaction depths. The relationship between the C/A ratios and the interaction depths can then be determined and used as the calibration. The calculation for our 3-D CdZnTe detectors shows that an 8% error in depth determination is incurred without the calibration.