Optimization of the Gain Layer Design of Ultra-Fast Silicon Detectors

The defining feature of Ultra-Fast Silicon Detectors (UFSD) is their gain layer design. In this paper, the performance of several types of gain layers, measured with a telescope instrumented with a $^{90}$Sr $\beta$-source, are reported. The sensors measured are produced by Fondazione Bruno Kessler (FBK) and by Hamamatsu Photonics (HPK). The FBK sensors feature three different gain layer designs, with boron and carbon co-implantation, and three sensor thicknesses (35, 45, and 55 $\mu$m), while the HPK sensors have two different gain layer designs (not carbonated) and two thicknesses (45 and 80 $\mu$m). The design yielding the best results, both when new and irradiated, is an FBK 45 $\mu$m-thick sensor with a carbonated deep gain layer where the carbon and the boron implants are annealed concurrently with a low thermal load. Exploiting the variety of designs presented in these productions, several additional studies on the UFSD working principles have also been performed.