Analytic response functions in compound semiconductor detectors

The absorbed energy distribution (A ED) in x-ray imaging detectors is an important factor that limits both energy resolution and image quality. In the diagnostic energy range (10120 ke V), escape of characteristic photons following photoelectric absorption and Compton scatter photons are primary sources of absorbed-energy dispersion in x-ray detectors. In this article, we describe the development of an analytic model of the AED of compound semiconductor detectors including the effects of escape and reabsorption of characteristic and Compton-scatter photons. We derive analytic expressions for semi-infinite slab geometry and validate our approach by Monte Carlo simulations using the commercial MCNPS^TM (ORNL, USA) code. In all cases, there was good agreement between analytic and Monte Carlo calculations. The analytic model allows us to obtain the 2D x-ray response matrix of arbitrary compound materials without time-consuming Monte Carlo simulations. We believe this model will be useful for correcting spectral distortion artifacts commonly observed in photon-counting applications and optimal design and development of novel x-ray detectors.