Spatial resolution for gamma ray interactions in stacks of monolithic silicon sensors

We are developing a new implementation of Compton imaging for nuclear medicine using a large volume of stacked monolithic silicon sensors. In this work we investigate how the spatial resolution is impacted by the pixel size, an important input to the design of the sensors. In general CMOS design is less challenging with larger pixels leaving more space for analog and digital electronics. On the other hand, spatial resolution is one of the key parameters that will impact the performance of the Compton imaging system. It is also important to consider the range of the recoil electron produced in Compton or photoelectric interactions, which impacts how accurately the interaction point can be estimated. The achievable resolution was evaluated with two interaction position reconstruction algorithms: one based on a Gaussian fit of the detected charge and a second based on the characteristic energy deposition along the electron track, with the former performing better at lower energies. Monte Carlo simulations were performed for 140 keV and 511 keV sources embedded in a water phantom, with pixel pitches ranging from 25 $\mu m$ to 250 $\mu m$. Energy-averaged in-plane resolution degraded from 8 $\mu m$ to 94 $\mu m$ as pixel size increased. The out-of-plane resolution was 216 $\mu m$ at low energies, limited by sensor thickness, and improved to 155 $\mu m$ at higher energies. The results suggest that pixel sizes in the order of 100 $\mu m$ can achieve spatial resolutions on the order of tens of micrometers.