The geometrical dependence of radiation hardness in planar and 3D silicon detectors

The radiation hardness of planar and 3D silicon detectors fabricated on Float-Zone and epitaxial silicon substrates is compared after exposure to neutron equivalent fluences greater than 10¹⁵ cm^-2. Following irradiation, the Signal Efficiency (SE), expressed as the ratio of the maximum signal after irradiation divided to the maximum signal before irradiation, is shown to depend only on the geometrical distance, L, between the p⁺ and n⁺ electrodes. The Signal Efficiency is independent of the silicon substrate used for the various detectors. A formalism describing the dependence of Signal Efficiency on L is derived and used to fit the data. The Signal Efficiency dependence on inter-electrode distance L and the fluence φ follow the same inverse proportionality law.