On drift fields in CMOS Monolithic Active Pixel Sensors with point-like collection diodes

- Paper withdrawn by the author - CMOS Monolithic Active Pixel Sensors for charged particle tracking are considered as technology for numerous experiments in heavy ion and particle physics. To match the requirements for those applications in terms of tolerance to non-ionizing radiation, it is being tried to deplete the sensitive volume of the, traditionally non-depleted, silicon sensors. We study the feasibility of this approach for the common case that the collection diodes of the pixel are small as compared to the pixel pitch. An analytic equation predicting the thickness of the depletion depth and the capacity of this point-like junction is introduced. We find that the predictions of this equations differs qualitatively from the usual results for flat PN junctions and that $dC/dU$-measurements are not suited to measure the depletion depth of diodes with point-like geometry. The predictions of the equation is compared with measurements on the depletion depth of CMOS sensors, which were carried out with a novel measurement protocol. It is found that the equation and the measurement results match with each other. By comparing our findings with TCAD simulations, we find that precise simulation models matches the empirical findings while simplified models overestimate the depletion depth dramatically. A potential explanation for this finding is introduced and the consequences for the design of CMOS sensors are discussed.