The spectral response of silicon X-ray detectors

A discrete analytic calculation of the spectral response of silicon drift detectors for X-rays is presented. The results are compared with measurements at BESSY II using monochromatic synchrotron radiation in the energy range from 0.2 to 2 keV. All Gaussian features (main, escape, and Al fluorescence peak) as well as the background are included in the model. The peak intensities are calculated from energy dependent probability distributions. The non-Gaussian background is produced by charge-loss in the entrance window. The charge loss of energetic photo and Auger electrons and the diffusion of low-energy secondary electrons into the aluminum dead layer are considered. The secondary electrons disperse in a Gaussian charge distribution with the width σsecσsec, which is the only free parameter of the model. All collected charge is summed up for every possible process and convoluted with electronic and Fano noise, yielding the energy distribution of the background. Its intensity is given by the probability of the process. This method generates all observed spectral background features using a single fundamental calculation scheme. It can, in principle, be applied to any type of semiconductor detector. The calculations are in very good agreement with the measurements.