Maximum-likelihood estimation for semiconductor detector arrays

We propose a rigorous statistical treatment of data from semiconductor detector arrays using maximum-likelihood estimation. For pixellated and cross-striped electrodes, a single gamma-ray interaction can produce signals in multiple electrodes. The set of signals generated from a single gamma-ray interaction are random variables with a probability law dependent on the position and energy of the gamma ray. If the signals are fixed then the probability law becomes the likelihood function. The maximum-likelihood estimate is then the position and energy that maximize the likelihood. We applied this estimator to a 48/spl times/48 pixellated CdZnTe array with 125 /spl mu/m pixel spacing. The likelihood law was evaluated with Monte-Carlo integration using a model of all physical processes affecting signal generation. By simplifying the physical model such that each gamma ray can undergo only one scattering process, computation time is greatly reduced with no measurable effect on energy resolution. The energy estimates formed histograms with 7.5 keV full-width-half-maximum (FWHM) at 140 keV, and 6 keV FWHM at 60 keV. Currently used methods show at best 11 keV FWHM at 140 keV and 9 keV FWHM at 60 keV. Comparison with simulations shows that these devices behave close to our model.