Accurate modeling of charge collection properties of small-pitch 3D pixel sensors based on Monte-Carlo simulations

The exceptional radiation hardness of small-pitch 3D pixel sensors has paved the way for their deployment in the innermost layers of both ATLAS and CMS for the High-Luminosity LHC upgrade. Developed using single-sided process, the fabrication technology of this type of sensors is now mature enough to explore smaller feature size layouts targeting 4D tracking applications, such as the VELO2 detector upgrade designed for LHCb. In view of these future upgrades, it is necessary to evaluate the sensors’ hit efficiency and timing resolution at pixel-level through the help of TCAD and Monte-Carlo simulations. A simplified approach based on 2D TCAD simulations is first presented; the results are then coupled with Monte-Carlo simulations to evaluate the in-pixel hit efficiency of the sensor under various operation conditions. Simulation results show a 100% hit efficiency before irradiation even at low reverse bias, which decreases after bulk damage. The results are in good agreement with the efficiencies measured on 3D sensor modules for the ATLAS Inner Tracker upgrade. To better account for the influence of different regions (e.g., the surface and the gap regions between the column tips and the backside), more comprehensive modeling approaches are introduced. They are based on segmenting the sensor into distinct parts to reduce the computational load of TCAD simulations. The corresponding maps are then extended and stitched together for subsequent simulations. These approaches have a more realistic approximation of the sensor structure and allow assessment of the efficiency in the gap region as well as the influence of surface damage.