Simulation and hit reconstruction of irradiated pixel sensors for the CMS experiment

In this paper a detailed simulation of irradiated pixel sensors was used to investigate the effects of radiation damage on the position determination and optimize the hit reconstruction algorithms. The simulation implements a model of radiation damage by including two defect levels with opposite charge states and trapping of charge carriers. The simulation shows that a position resolution below 15 $\mu$m along the CMS $r-\phi$ plane can be achieved after an irradiation fluence of $5.9\times10^{14}$ n$_{\rm{eq}}/$cm$^2$. In addition, we show that systematic errors in the position determination can be largely reduced by applying $\eta$ corrections.