Estimation methods for semiconductor gamma-ray detectors

Abstract

Gamma-ray detectors based on high-density semiconductors, such as cadmium zinc telluride, are being developed for applications in nuclear medicine, astronomy and the monitoring of nuclear weapons material. In contrast to the more commonly used scintillators, which convert gamma-ray energy into light, semiconductors directly convert the energy of a gamma ray into electrical current. This direct conversion often leads to the perception that gamma-ray detection in semiconductors is not an estimation problem. This dissertation presents the contrasting view that gamma-ray detection in semiconductors is fundamentally an estimation problem, and it is only through the appropriate analysis of gamma-ray signals that optimal energy resolution and spatial resolution can be achieved. To estimate interaction parameters, such as the energy of the gamma ray and its interaction position, it is first necessary to have an accurate model of the detector system. In this work, the system consists of slabs of CdZnTe with arrays of pixel electrodes mounted on integrated readout circuits. A theoretical model of detector behavior is presented, including a new model for charge spreading in the detector. Methods for experimentally determining detector behavior are developed based on mapping detectors with narrow beams of gamma rays. Estimating the interaction positions and energies proceeds from a statistical model of the production of pixel signals, derived from our physical model. Energies and interaction positions are estimated by maximizing the likelihood function. The likelihood is the probability that a gamma ray with a given position and energy will produce an observed set of pixel signals. This maximum-likelihood estimation improves the energy resolution over simpler methods and can give the interaction position in three dimensions. A likelihood function can be calculated for an entire set of gamma rays, in which case an image can be estimated from the raw data without ever estimating individual interaction positions and energies. The Expectation-Maximization algorithm is used to reconstruct images and energy spectra by maximizing the ensemble likelihood function. In this work, the list-mode form of the algorithm is used, meaning that the raw data consist of lists of pixel signals for each gamma ray. Both spatial and energy resolution improve when this algorithm is applied to the raw pixel signals.