Numerical simulations of 3D positioning in cross-strip Ge detectors

We have numerically simulated the charge collection curves in an 11-mm thick, 2-mm pitch cross strip Ge detector to determine the intrinsic and expected performance or using relative anode and cathode signal timing to determine the interaction depth in the detector. This technique will allow full 3D positioning in large volume GeDs. We have calculated the detailed electric field inside the detector using relaxation techniques and taking into account the surface conductivity in the gap between strips. The weighting field for the detector has also been calculated for determining the charge induced on the electrode for any position within the detector. These two fields have then been used in charge collection simulations to trace electron-hole pairs from the interaction site to the signal electrodes, calculating the induced signals on the anode and cathode for each time step. Using this simulation, we can determine the relative difference in charge collection times between the anode and cathode as a function or position in the detector, allowing us to determine the intrinsic variation in the timing signal at each depth in the detector, which will set a limit on our ability to determine the interaction depth. By including a random noise based on that modeled from a real detector, we can determine the expected depth resolution as a function of depth in the detector.