## 3 The Timepix3 Radiation Monitor
### Operational Principle: Signal Formation  
When traversed by ionising particles, the silicon sensor of the Timepix3 Radiation Monitor generates output current pulses according to the Shockley-Ramo theorem [40; 41; 42] by collecting the free charge carriers (electrons and holes) released in each pixel. In particular, the charge carriers collected by the pixel electrodes are those released in the active portion of the detector with thickness \(W\), defined as the region where an electric field \(\vec{E}\) is maintained via the application of the bias voltage \(V_{bias}\). The operational principle of the Timepix is that the energy deposited in the pixel is proportional to the number of charge carriers collected by the electrodes, which is, in turn, proportional to the time that it takes to discharge the electrodes via a constant current. The amplified output current pulse of the pixel is shown schematically in Figure 3, along with the timing structure of the Timepix3. When the output signal exceeds a pre-set threshold, a global 40 MHz clock measures the time that it takes for the signal to return below it, i.e., the time-over-threshold (ToT), expressed in clock units (where one time unit corresponds to 25 ns, as determined by the clock frequency). Asynchronously, a local 640 MHz clock starts when the signal exceeds the threshold, thereby defining the fast time-of-arrival (fToA). The clock is stopped by the rising edge of the 40 MHz clock, at which moment the time-of-arrival (ToA) is registered. The Timepix3 Radiation Monitor uses a p-on-n silicon sensor, with the negative electrodes connect to the analogue front-end, and as such the charge carriers are holes, as shown in Figure 4. Moreover, the module is operated with a partial bias voltage of \(V_{bias}=50\) V, leading to a partially depleted sensor thickness of approximately \(W=250\) um,  
Figure 2: (**Left**) Timepix3 setup layout diagram, showcasing the intended operation with the laptop, back-end and power supplies in a no radiation area, the front-end crate that should be radiation tolerant, and the in-beam. (**Right**) Timepix3 detector module, hosting the detector. computed with the method described in Ref. [35]. Both these choices lead to a relatively long signal collection time, because the mobility of holes in silicon is three times smaller compared to electrons, and the partial bias voltage leads to a lower electric field \(\vec{E}\) in the depleted region. Quantitatively, while the charge collection times can typically be around \(\mathcal{O}(10\,\mathrm{ns})\), for the Timepix3 Radiation Monitor it is expected to rise to \(\mathcal{O}(100\,\mathrm{ns})\). The longer (longitudinal) charge collection time also allows for more diffusion to occur (at a constant diffusion velocity \(v_{diff}\)), leading to an increased spread of the charge carriers in the transversal plane. In the case of a pixellated detector structure, this lateral spread causes charge sharing among the chip electrodes, and many pixels could have a signal above threshold; that is, charge carriers generate a cluster of adjacent pixels, as shown exemplarily in Figure 5 for a \(5.6\,\mathrm{MeV}\) alpha particle hitting perpendicularly the detector, for which a 2D Gaussian shape is typically assumed [29; 43; 44]. The implications of this feature on the reconstruction of particle hits is further discussed in the next sections. Figure 4: **(Left)** Timepix3 detector geometry (not to scale), with a known \(500\,\mathrm{nm}\) aluminium metalisation layer and an unknown dead layer on top, as well as the depletion layer \(W=250\,\mathrm{\SIUnitSymbolMicro m}\) smaller than the detector thickness \(D=300\,\mathrm{\SIUnitSymbolMicro m}\), indicating as well the direction of the charge carrier collection. **(Right)** Proton and alpha particles range and stopping power in silicon in the energy range of the 3 MV Tandem accelerator at CNA. Data taken from Ref. [45]. The horizontal grey area starts at \(250\,\mathrm{\SIUnitSymbolMicro m}\), indicating the depletion region thickness.