Simulation of guard ring influence on the performance of ATLAS pixel detectors for inner layer replacement

Electric field magnitude and depletion in the bulk of silicon pixel detectors, which influence its breakdown behaviour, was studied using finite-element method to solve the drift-diffusion equation coupled to Poisson's equation in a simplified two dimensional model of the ATLAS pixel sensor. Based on this model, the number of guard rings and dead edges width were modified to investigate their influence on the detector's depletion at the edge and on its internal electrical field distribution. Final ly, the 3 level model was implemented into the simulation to study the behaviour of such detector under different level of irradiation.