The development of n-on-p edgeless planar pixel sensors being fabricated at FBK (Trento, Italy), aimed at the upgrade of the ATLAS Inner Detector for the High Luminosity phase of the Large Hadron Collider (HL-LHC), is reported. A characterizing feature of the devices is the reduced dead area at the edge, achieved by adopting the active edge technology, based on a deep etched trench, suitably doped to make an ohmic contact to the substrate. The project is presented, along with the active edge process, the sensor design for this first n-on-p production and a selection of simulation results, including the expected charge collection efficiency after radiation fluence of $1 times 10^{15} {rm n_{eq}}/{rm cm}^2$ comparable to those expected at HL-LHC (about ten years of running, with an integrated luminosity of 3000 fb$^{-1}$) for the outer pixel layers. We show that, after irradiation and at a bias voltage of 500 V, more than 50% of the signal should be collected in the edge region; this confirms the validity of the active edge approach.
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