Transient Monte Carlo simulations for the optimisation and characterisation of monolithic silicon sensors

An ever-increasing demand for high-performance silicon sensors requires complex sensor designs that are challenging to simulate and model. The combination of electrostatic finite element simulations with a transient Monte Carlo approach provides simultaneous access to precise sensor modelling and high statistics. The high simulation statistics enable the inclusion of Landau fluctuations and production of secondary particles, which offers a realistic simulation scenario. The transient simulation approach is an important tool to achieve an accurate time-resolved description of the sensor, which is crucial in the face of novel detector prototypes with increasingly precise timing capabilities. The simulated time resolution as a function of operating parameters as well as the full transient pulse can be monitored and assessed, which offers a new perspective on the optimisation and characterisation of silicon sensors. In this paper, a combination of electrostatic finite-element simulations using 3D TCAD and transient Monte Carlo simulations with the Allpix framework are presented for a monolithic CMOS pixel sensor with a small collection diode, that is characterised by a highly inhomogeneous, complex electric field. The results are compared to transient 3D TCAD simulations that offer a precise simulation of the transient behaviour but long computation times. Additionally, the simulations are benchmarked against test-beam data and good agreement is found for the performance parameters over a wide range of different operation conditions.