Simulation of signals in ultra radiation-hard silicon pixel detectors

A detailed simulation of silicon pixel detectors irradiated to very high fluences, in the range foreseen for vertex detectors after the Large Hadron Collider luminosity upgrade, is presented. The charge collection properties and the detector response were computed for different silicon materials (standard float zone, diffusion oxygenated float zone, Czochralski, epitaxial silicon) and operating conditions. At the maximum fluence ($10^{16} \rm{n}_{eq}/cm^{-2}$) the signal is limited by charge trapping rather than by the thickness of the active volume. Since all the silicon materials studied so far have a similar trapping cross section, they are all expected to collect a signal of 2000-2500 electrons at 600 V bias voltage. A detection threshold of 1000-1200 electrons is required in order to have a 97% detection efficiency.