## 3 The Timepix3 Radiation Monitor
### Pixel Level Energy Calibration Principles  
In order to measure the deposited energy in each pixel, a calibration procedure of the Timepix3 Radiation Monitor must be performed, deriving the relation between the output  
Figure 5: Example of a full 5.6 MeV alpha cluster evolution. The particle hits just one pixel at perpendicular incidence in pixel \((x,y)\) = (157,229) and the charges diffuse to adjacent pixels over time, leading to clusters with more pixels. The timing information refers to the combined ToA (40 MHz, or 25 ns) and fast ToA (640 MHz, or 1.5625 ns) counters, when the charge first exceeds the threshold (as shown in Figure 3), and it is uncorrelated with the ToT that is read at the end, when the signal falls below the threshold.  
ToT value in each pixel to the corresponding deposited energy \(E_{dep}\)[22; 24] (the energy deposited in the sensor can be expressed directly in keV or in the number of electron-hole pairs produced, knowing that the average energy required to produce an electron-hole pair in silicon is \(\sim\)3.6 eV), while the exact calibration depends on the operational parameters of the module, notably the threshold level and the bias voltage, general features of the pixel-level ToT vs. energy calibration have been identified in the literature [24], as illustrated qualitatively in Figure 6, where different regions with distinct features can be isolated.  
At a low deposited energy, the Timepix3 Radiation Monitor measures non-zero ToT only if a threshold \(E_{thres}\) is exceeded (set by an operational voltage of 0.57 mV for the detector in this paper, corresponding to a threshold of 5.3 keV). Above \(E_{thres}\), there is an initial range (labelled as Region A in the figure) where the ToT response increases in a non-linear way [20; 21], typically spanning over a few keV, whereas for higher deposited energies, the Timepix sensors are known to present a wide region of linear response (Region B), which typically extends up to several hundred keV (e.g., 850 keV as found in Ref. [24]). Above a characteristic energy labelled as \(E_{sat}\), the ToT calibration curve exhibits a saturation-like effect in the form of a knee (Region C) [22; 23; 25], above which a parabolic-like increase in the ToT as a function of the deposited energy is reported (Region D) [24]. Lastly, at even higher energies, the ToT is known to decrease as a function of the deposited energy (Regions E and F), leading to ambiguities in the Timepix energy deposition measurements and complex effects [51; 52].  
Owing to its linearity, Region B represents an ideal range of operation for the Timepix3 Radiation Monitor, whereas all regions below or above it introduce non-linear or multiple-valued effects, particularly when going beyond Region D. In fact, an essential question to be answered by this work is whether the mixed radiation field of CERN accelerators, for which the detector is envisaged, yields energy depositions per pixel that fall (at least for the overwhelming part of the radiation field composition) within the boundaries of Region B, as further discussed in Section 6. For now, it is anticipated that this is mostly the case; therefore, the calibration campaign presented in this paper was specifically targeted at the linear Region B and possibly at the first saturation effects (Region C), neglecting the higher-energy regions as well as the low-energy one (Region A).