## 5 Results
### Energy Calibration and Dead Layer Estimation  
The cluster ToT volume data presented above serve as the basis for the Timepix3 Radiation Monitor calibration, obtained via the procedure outlined in Section 3.5, and supported by the estimation of the silicon front dead layer. Along with the ToT data, FLUKA simulations are employed to quantify the energy deposited \(E_{dep}\) in the sensor from a beam of particles \(E_{0}\) via Equation (2), such that one takes into account the energy lost in the aluminium metalisation layer, with a known thickness of 500 nm, and in the dead layer, with a thickness to be evaluated via the angular scan. As previously mentioned, the sensor calibration and the dead layer estimation have been obtained via an iterative process. The calibration is expressed via Equation (1), where the parameters \(a\) and \(b\) are derived by performing a linear fit that uses only the four lowest energy data points (three for protons and one for alphas, up to 1 MeV) to ensure that the values are not affected by high-energy saturation effects. For all energies, a first calibration is derived by assuming that the thickness of the silicon dead layer is null. This first calibration result is used as an input to obtain a first evaluation of the dead layer, from the data of the angular scan and via Equation (5). Subsequently, the calibration is recomputed using FLUKA simulations with the updated dead layer thickness, repeating the procedure until stable values of \(T_{DL}\), \(a\), and \(b\) are reached, after just six iterations, as shown in Figure 12.  
At the end of the iterative process, the linear fit of \(E_{dep}\) as a function of \(1/\cos\theta\) shown in Figure 11 is the following:  
\[E_{dep}\ [\mathrm{keV}]=(598\pm 68)\ [\mathrm{keV}]-(51.5\pm 5.8)\frac{1}{ \cos\theta}\ [\mathrm{keV}], \tag{6}\]  
where the uncertainty on the fit parameters is included. Using Equation (5), and considering a stopping power of \(dE/dx|_{Si}(E_{0}-E_{dep,Al})=56.45\,\mathrm{MeV}\,\mathrm{\SIUnitSymbolMicro m}^ {-1}\) for 0.6 MeV protons in silicon (from [45]), the dead layer thickness is obtained as follows:  
Figure 11: (**Left**) Timepix3 measurements for proton runs at 597 keV swiping through incident angles from 0\({}^{\circ}\) to 45\({}^{\circ}\), displaying a (**Right**) deposited energy variation that can be fitted with a straight line against the inverse of the irradiation angle cosine. \[T_{DL}=333\pm 38(\sigma_{fit})\pm 17(\sigma_{dE/dx})\pm 4(\sigma_{\theta})\pm 1( \sigma_{ToT})\ \mathrm{nm} \tag{7}\]  
which includes uncertainties associated with the fit parameters (\(\sigma_{fit}\)), the assumption of a constant stopping power (\(\sigma_{dE/dx}\)), for which a 5% error is considered (see Section 4.2), the measurement of the angle (\(\sigma_{\theta}\), assuming a 1% accuracy on \(\theta\)), and the error on the mean of the Guassian peaks in the measured ToT data (\(\sigma_{ToT}\)). The measured silicon dead layer of 333 nm is in line with the expectations, as other silicon detectors have dead layers of the order of 500 nm [56; 57]. For the above value of the silicon dead layer thickness, the FLUKA code is used to evaluate the deposited energies in each layer of the Timepix3 Radiation Monitor during the irradiations with orthogonal angle, as presented in Table 1 along with the measured average number of pixels per cluster \(N\) for each energy and particle type. The simulations indicate that alpha particles are losing a larger fraction of their energy in the front layers of the sensors (up to 23.3%) compared to protons with the same initial energy due to their higher stopping power.