Signal and noise of Diamond Pixel Detectors at High Radiation Fluences

CVD diamond is an attractive material option for LHC vertex detectors because of its strong radiation-hardness causal to its large band gap and strong lattice. In particular, pixel detectors operating close to the interaction point profit from tiny leakage currents and small pixel capacitances of diamond resulting in low noise figures when compared to silicon. On the other hand, the charge signal from traversing high energy particles is smaller in diamond than in silicon by a factor of about 2.2. Therefore, a quantitative determination of the signal-to-noise ratio (S/N) of diamond in comparison with silicon at fluences in excess of 10$^{15}$ n$_{eq}$ cm$^{-2}$, which are expected for the LHC upgrade, is important. Based on measurements of irradiated diamond sensors and the FE-I4 pixel readout chip design, we determine the signal and the noise of diamond pixel detectors irradiated with high particle fluences. To characterize the effect of the radiation damage on the materials and the signal decrease, the change of the mean free path $\lambda_{e/h}$ of the charge carriers is determined as a function of irradiation fluence. We make use of the FE-I4 pixel chip developed for ATLAS upgrades to realistically estimate the expected noise figures: the expected leakage current at a given fluence is taken from calibrated calculations and the pixel capacitance is measured using a purposely developed chip (PixCap). We compare the resulting S/N figures with those for planar silicon pixel detectors using published charge loss measurements and the same extrapolation methods as for diamond. It is shown that the expected S/N of a diamond pixel detector with pixel pitches typical for LHC, exceeds that of planar silicon pixels at fluences beyond 10$^{15}$ particles cm$^{-2}$, the exact value only depending on the maximum operation voltage assumed for irradiated silicon pixel detectors.