A fitting model of the pixel response to monochromatic X-rays in photon counting detectors

We present a simple fitting model for the pixel response to monochromatic X-rays in single photon counting pixelated detectors that takes into account the 2D effects of the charge sharing and of the electronic noise on the photon counting process. It is based only on geometrical and physical parameters such as the pixel size, the charge cloud size at the pixel depth and the total electronic noise of the front-end circuitry. The equations describing the pixel point spread function and the integral pulse height spectrum are derived preserving the genuine 2D nature of the charge collection process. The fitting performances of the model has been assessed on a set of experimental integral pulse height spectra measured with an IBEX photon counting ASIC bonded to a 450 mu m thick Silicon sensor with 75 mu m x 75 mu m pixel size, irradiated with monochromatic X-rays in the energy range 6-12.4 keV, with excellent agreement between model and measurement. The actual contributions of the charge sharing and of the electronic noise are identified and estimated. As a possible consequence, the model can be used to predict precisely the behavior of photon counting detection systems as a function of the design parameters.