  Combining electrostatic field simulations with Monte Carlo methods enables
realistic modeling of the detector response for novel monolithic silicon
detectors with strongly non-linear electric fields. Both the precise field
description and the inclusion of Landau fluctuations and production of
secondary particles in the sensor are crucial ingredients for the understanding
and reproduction of detector characteristics.
  In this paper, a CMOS pixel sensor with small collection electrode design,
implemented in a high-resistivity epitaxial layer, is simulated by integrating
a detailed electric field model from finite element TCAD into a Monte Carlo
based simulation with the Allpix$^2$ framework. The simulation results are
compared to data recorded in test-beam measurements and very good agreement is
found for various quantities such as cluster size, spatial resolution and
efficiency. Furthermore, the observables are studied as a function of the
intra-pixel incidence position to enable a detailed comparison with the
detector behavior observed in data.
  The validation of such simulations is fundamental for modeling the detector
response and for predicting the performance of future prototype designs.
Moreover, visualization plots extracted from the charge carrier drift model of
the framework can aid in understanding the charge propagation behavior in
different regions of the sensor.
