Experimental Study and Empirical Modeling of Long Term Annealing of the ATLAS18 Strip Sensors

In order to continue the program of the LHC, the accelerator will be upgraded to the High Luminosity LHC (HL-LHC), which will have a design luminosity of $5 \times 10^{34} cm^{-2}s^{-1}$ , an order of magnitude greater than the present machine. In order to meet the occupancy and radiation hardness requirements resulting from this increase in luminosity, the present ATLAS tracking detector must be replaced. The ATLAS Collaboration is constructing a new central tracking system based completely on silicon sensors. In order to satisfy the radiation hardness requirements we have developed a new n-in-p sensor design. Extensive studies have shown that it results in detectors which comfortably reach the required end-of-life performance. The latest sensor layouts prepared for preproduction, known as ATLAS18, implement this design. However, as well as knowing the performance after a given irradiation fluence, operational considerations require an understanding of the time development of the annealing and resulting variation of the collected charge, of irradiated detectors at different temperatures. Here we describe the measurement of charge collection performance as a function of irradiated fluence and long term annealing time. We also describe a semi-empirical model based on these measurements which allows us to predict the end-of-life charge collection as a function of the temperature profile during operation of the detector. The use of the model to study the effect of annealing on the strip detector at a radius of 40 cm and an integrated irradiation fluence of $\textrm{1.6} \times \textrm{10}^{15} \ \textrm{24}~\textrm{MeV}~\textrm{neutron}~\textrm{ equiv}~\textrm{cm}^{-2}$ is presented.