Simulating monolithic active pixel sensors: A technology-independent approach using generic doping profiles

The optimisation of the sensitive region of CMOS sensors with complex non-uniform electric fields requires precise simulations, and this can be achieved by a combination of electrostatic field simulations and Monte Carlo methods. This paper presents the guiding principles of such simulations, using a CMOS pixel sensor with a small collection electrode and a high-resistivity epitaxial layer as an example. The full simulation workflow is described, along with possible pitfalls and how to avoid them. The presented method provides an optimisation tool that is sufficiently accurate to investigate sensor behaviour and trade-offs of different sensor designs without knowledge of proprietary information.

The workflow starts with detailed electric field finite element method simulations in TCAD, using generic doping profiles. Examples of the effect of varying different parameters of the simulated sensor are shown, as well as the creation of weighting fields, and transient pulse simulations. Using this, a realistic working geometry representing the investigated sensors is determined. The fields resulting from TCAD simulations can be imported into the ${\mathrm{Allpix}}^2$ Monte Carlo simulation framework, which enables high-statistics simulations. Example Monte Carlo simulation setups are presented and the different parts of a simulation chain are described.

Simulation studies from small collection electrode CMOS sensors are presented, and example results are shown for both single sensors and multiple sensors in a test beam telescope configuration. The studies shown are those typically performed on sensor prototypes in test beam campaigns, and a comparison is made to test beam data, showing a maximum deviation of 4% and demonstrating that the approach is viable for generating realistic results. The presented simulation procedure thus proves a useful tool for sensor research and development.