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Abstract

The pursuit of increasingly rare processes with higher precision in modern high-energy particle physics experiments drives the development of silicon pixel detectors offering excellent spatial and timing resolution, radiation hardness, and minimal material budget. However, a lower material budget necessitates thinner detectors, which provide less active volume for energy deposition, thereby reducing the signal-to-noise ratio. A promising approach is represented by HV-MAPS (High-Voltage Monolithic Active Pixel Sensor). These monolithic pixel sensors integrate the active pixel matrix and readout electronics on a single die, allowing the silicon sensors to be thinned down to 50 μm. The sensor studied in this work is the MuPix10, a full-reticle prototype of about 2×2 cm^2, developed for the Mu3e experiment. Each pixel features a large fill factor electrode design of a deep n-well embedded in a low to medium resistivity p-substrate. HV-MAPS are generally biased from the top through guard-ring structures, and cannot be operated beyond full depletion. However, variations in substrate resistivity and manufacturing tolerances lead to varying depletion depths across sensors, mandating a better understanding of charge collection in under-depleted operation. To investigate the corresponding charge collection spectrum, a dedicated testbeam campaign was performed using 350 MeV c^−1 pions. This is done for different sensor thicknesses, ranging from 50 μm to 100 μm, as well as substrate resistivities and reverse bias voltages. By measuring the hit efficiency as function of the applied detection threshold, the integrated charge spectrum is reconstructed. To unfold the impact of detector effects on these measurements, a dedicated calibration procedure was developed based on charge injection to the pixel electronics and Fe-55 source measurements for absolute charge calibration. The charge spectrum is modeled by a convolution of a Landau distribution with a normal distribution to account for energy deposition fluctuations and detector effects, respectively. This approach has been evaluated using simulated charge deposition spectra and has proven to be valid even for thin silicon sensors. By applying theoretical predictions for the scale and the most probable energy loss for incident particles of known kinematics, the effective charge deposition thickness can be extracted. The measured charge collection exceeds expectations based solely on the depleted region, indicating that the non-depleted volume significantly contributes to the charge collection in under-depleted operation. Even for low bias voltages, where charge losses due to charge sharing are expected, the observed charge collection exceeds the depleted thickness expectation. Comparing an almost fully depleted 50 μm sensor with a 100 μm sensor at −20 V shows a 40 % higher most probable charge collection, corresponding to an excess effective deposition thickness of about 12 μm. The relative excess observed under equivalent bias conditions increases with the sensor thickness, implying that the size of the non-depleted region governs the overall charge collection behavior in this thickness range. This suggests that even in thicker sensors, a notable fraction of the non-depleted region participates in charge collection.