Radial dependence of induced current density and small pixel effect in parallel-plate detectors

Now, pixelated detectors have a wide application in X-ray and gamma-astronomy, nuclear spectroscopy and nuclear medicine. If the absorption of charge carriers is high as in compound semiconductors, the process of charge induction on pixelated electrodes determines the spatial resolution of these detectors. Shockley-Ramo theorem gives only the total charge induced on the electrode of a parallel-plate detector. In this work the exact analytical solution for the radial dependence of induced current density on the electrodes was found. The formula for the charge induced on the right and the on the left electrodes in a circle of a given radius was also derived. The calculated dependence of the charge induced by a charged particle on the electrodes demonstrates the small pixel effect, which has its explanation in the behavior of the radial dependence of the induced charge.