# Lineal Energy of Proton in Silicon by a Microdosimetry Simulation
## 3 Results and Discussions
### Lineal Energy Contribution from Various Secondary Species  
Since Single Event Rate (SER) is a function of LET [39], or \(y\) in this study, it is important to understand the \(y\) contribution from various secondary species for radiation hardening design. Figure 3 shows the \(y\) spectra of various types of secondary particles in pure silicon irradiated with 200 MeV protons. The \(y\) spectra in silicon irradiated by a 200 MeV proton beam in this study was quite different from the results from [PERSON] [40] and [PERSON] [8]. In [PERSON] [40] and [PERSON] [8], their LET has a cut off around 15-16 MeV-cm\({}^{2}\)/mg. However, there are few events with \(y\) as high as 60 MeV-cm\({}^{2}\)/mg as observed in our study. Furthermore, the spectra in their studies have a plateau before 10 MeV-cm\({}^{2}\)/mg and drop rapidly after 10 MeV-cm\({}^{2}\)/mg. In our case, the counts dropped quickly before 2 MeV-cm\({}^{2}\)/mg, and it became a straight line from 2 to 25 MeV-cm\({}^{2}\)/mg, followed by a long tail after 25 MeV-cm\({}^{2}\)/mg. To better understand the above-mentioned discrepancies, the \(y\) spectrum was separated by different contributors with various \(Z\) values. For \(y<2\) MeV-cm\({}^{2}\)/mg, the major contributors are particles with \(Z=1\) and 2. As they are light ions, their contributions to LET spectra dropped sharply and disappeared for \(y>10\) MeV-cm\({}^{2}\)/mg. For \(y\) between 2 and 10 MeV-cm\({}^{2}\)/mg, the contribution is mixed with low \(Z\) and high \(Z\) secondaries. In this region, contributions from low \(Z\) secondaries decrease sharply and high \(Z\) secondary particles became major contributors after \(y>5\) MeV-cm\({}^{2}\)/mg. These high \(Z\) secondaries were from heavy ions generated by (p, x) reactions. The \(y\) distribution of high \(Z\) secondaries had a peak around \(y=5\) MeV-cm\({}^{2}\)/mg with few counts in low \(y\) and a long tail in the high \(y\) region, extending to 50 to 60 MeV-cm\({}^{2}\)/mg. Therefore, the overall \(y\) spectra of 200 MeV proton irradiated on silicon can be separated into three parts as follows. First part is \(y<2.5\) MeV-cm\({}^{2}\)/mg contributed from light ions; second part is 5 MeV-cm\({}^{2}\)/mg \(<y<10\) MeV-cm\({}^{2}\)/mg contributed by a mixture of both light and heavy ions and third part is \(y>10\) MeV-cm\({}^{2}\)/mg contributed only by heavy ions. In contrast to the works of [PERSON] et al. and [PERSON] et al. [8; 40], the LET spectra of their studies have a cut off around 15-16 MeV-cm\({}^{2}\)/mg but not in our study. This difference of our work and their work is because [PERSON] and [PERSON] used a reference Table to calculate the LET from energy fluence instead of calculating the energy deposition, and such method is only applicable for large target where the number of interactions is large enough that \(y\) can convergence to a single value which is LET. Unfortunately, in tiny SV, the \(y\) distribution is quite board when the SV is thin and using single expected value of LET becomes meaningless. Moreover, the reference Table used in their study has the cut off around 15-16 MeV-cm\({}^{2}\)/mg. The differential fluences for LET \(<\) 5 MeV-cm\({}^{2}\)/mg are significantly different between our results and those of [PERSON] et al. [8]. In Figure 7 of [PERSON]'s work. the differential fluence is around 3000/10\({}^{10}\) incident protons at LET = 1 MeV-cm\({}^{2}\)/mg and 1000/10\({}^{10}\) at 5 MeV-cm\({}^{2}\)/mg. However, in our study, the differential fluence is 2400/10\({}^{10}\) at 1 MeV-cm\({}^{2}\)/mg and 360/10\({}^{10}\) at 5 MeV-cm\({}^{2}\)/mg as shown in the Figure 4. The slope in our study is about twice that of the [PERSON]'s result because [PERSON] et al. did not consider the light secondaries such as protons and helium. In our study, the \(y\) contribution from each specific secondary particle is separate recorded, and they are plotted in Figure 5, where the proton and helium contribute more than 99% of the events in the region of \(y<\) 5 MeV-cm\({}^{2}\)/mg.