Generalization of the modeling and design considerations of concentric and spiral Si drift detectors

The one-dimensional design consideration for the spiral (cylindrical geometry) Si drift detector (SDD) described in literature [1], [2] has been modified and generalized also for small drift distance (R) compatible to the detector thickness (d), i.e. for R∼d, and for non-uniform backside biasing situations. With smaller R, an array of SDD with small pixel size down to a few hundreds of microns will be possible. Also, by applying a non-uniform biasing voltage with a gradient similar (proportional) to the front side, one can increase the reach-through voltage, resulting in a large drift field for carriers. This can be important for large R (>3 mm), or for high resistivity Si substrates (>8 kΩ cm). In the modeling, the one-dimensional solution to solve the electric potential and drift field, as well as the spiral design have been modified and generalized for all cases. The previous solution in the literature is an approximation of this work for R⪢d.