Count rate statistics for drift detectors

Solid state drill detectors have emerged as a promising technology for high count-rate, high energy-resolution applications, e.g. X-ray spectroscopy and inelastic scattering experiments at synchrotron light sources. In such devices, the charge carriers generated from the absorption of a photon in the detector medium are made to drift through a region that has an electric field defined by field shaping electrodes before approaching and inducing a signal on a sensing electrode. Since all charges drift to this one location, there is a time delay between the occurrence of an event (absorption of a photon) and the generation of the electrode signal which is dependent on the position of the event. In this work, we consider what effect this has on the pile-up statistics. We derive expressions for the cases of a continuous X-ray source, a pulsed source with period that is either much less than the shaper support time or much less than the average drift time, and a pulsed source with a period that is long or comparable to both the shaper support and the drift time.