Observation, modeling, and temperature dependence of doubly peaked electric fields in irradiated silicon pixel sensors

We show that doubly peaked electric fields are necessary to describe grazing-angle charge collection measurements of irradiated silicon pixel sensors. A model of irradiated silicon based upon two defect levels with opposite charge states and the trapping of charge carriers can be tuned to produce a good description of the measured charge collection profiles in the fluence range from 0.5×1014 to 5.9×1014neq/cm2. The model correctly predicts the variation in the profiles as the temperature is changed from -10 to -25∘C. The measured charge collection profiles are inconsistent with the linearly varying electric fields predicted by the usual description based upon a uniform effective doping density. This observation calls into question the practice of using effective doping densities to characterize irradiated silicon.