  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 Squared
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.
