Combining TCAD and Monte Carlo Methods to Simulate CMOS Pixel Sensors with a Small Collection Electrode using the Allpix$^2$ Framework

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.