# Lineal Energy of Proton in Silicon by a Microdosimetry Simulation
## 2 Simulation Setup  
The simulation in this study is based on Geant4 10.05 [16]. The physics model of electromagnetic processes in this simulation is aligned with G4 EmStandardPhysics_option4. For electrons, due to their low LET, they cannot contribute to high \(y\) effects [30], and thus the step function (parameter for step size \(R\)) can be set such that \(R\) over range = 0.01 and final range = 1 nm to speed up the simulation. For hadrons that have high LET and they are therefore more important in this study, the R over range = 0.00001 and the final range = 0.1 nm are set to improve the accuracy while keeping the efficiency of the Monte Carlo simulation. For the intranuclear cascade, the [PERSON]'s model is widely used [31]. The nucleon spectra from continuum-state transitions for protons on complex nuclei are calculated using the intranuclear-cascade approach. However, the model is commissioned in high-energy physics. An alternative method is a detailed three-dimensional model of the nucleus, and is based exclusively on the binary scattering between reaction participants and nucleons within this nuclear model, called binary cascade model [32]. [PERSON] et al. showed that, at a few hundreds of MeV, the binary cascade model can predict the secondary particles yields comparable to experimental data effectively [33; 34]. Additionally, there are several evaluated and experimental nuclear cross-section data banks, such as TENDL [35], EXFOR [36] and JEFF [37] which are precise but they are only for limited materials. The intra-nuclear model, which controls secondary yields, will be compared in Geant4 using two different models. The Bertini cascade model which is widely used in SEEs studies, and the binary cascade which is found to be better for incident particles of several hundreds of MeV [34]. In addition, this work also considers the impact of high precision (HP) model using the JEFF 3.3 extension cross-section table. The geometry in this project is a Multi-layer cylinder as shown in Figure 1. The diameter of the cylinder is 1 mm in order to ensure that most secondaries will not go out of the boundary. A 30-\(\mu\)m of pure silicon layer is used to generate secondary particles. Under the silicon layer is the sensitive volume (SV). The SV thickness was used to calculated lineal energy instead of mean chord length in the study. As described previously, the mean chord length concept is used better for randomly oriented chords in a given volume. The primary particles simulated in this study do not have isotropic distribution, and they are mostly incident perpendicular to the SV. Although ICRU report 36 [22] recommended using 4 _V/A_ to calculate mean chord length, [PERSON] and [PERSON] [38] found that real average path length was smaller than mean chord length for non-isotropic irradiation. If we calculated mean chord length according to the 4 _V/A_ approach, the mean chord length of our SV with 1 mm diameter and 100 nm thickness will be 200 nm. However, the average track length in this thickness from the simulation is 104.9 nm, which is less than 5% difference to the SV thickness. Hence we use the SV thickness instead of the mean chord length to calculate \(y\). The species and kinetic energy of each particle entering the SV are recorded as secondaries. The energies imparted from all the tracks crossing through the SV are summed up and divided by the thickness of SV to calculate the lineal energy (\(y\)). To compare the effect of SV thickness, six thicknesses, namely 1, 10, 30, 100, 1000 and 10,000 nm are simulated. Figure 1: The geometry setup in this study. The silicon is with natural isotope abudence, density is 2330 mg/cm\({}^{3}\) and mean extiation potetial I = 173 eV. In addition, the lineal energy and secondary particle yields from the thickness of 100 nm results are further used to compared with the results from [PERSON] et al. for compatibility investigation.