A New Method for Precisely Designing the Spiral Structure of an SDD with Optimal Electrical Properties

To improve accuracy in calculating the radius of a spiral electrode and the number of turns in existing spiral-type Silicon Drift Detectors (SDDs), in this paper, we propose a method with which to derive first- and second-order approximations of differentiation equations for the spiral angle θ as a function of its radius r(θ) using Taylor expansion. Combining these with formulas for electrode pitch P(r) and width W(r), we developed a simple and physically intuitive method for obtaining a high-precision single-sided hexagonal spiral SDD. Comparisons of spiral structures calculated using the first- and second-order approximation formulas reveal that the second-order approximation yields more spiral turns, thus allowing superior electrical performance, including smoother electric potential profiles, more-uniform electric field distributions, and better-defined electron drift channels.