## 2 Materials and Methods
### Monte Carlo Simulation  
To simulate the LETs and secondary particle yields in semiconductor devices, Geant4 10.04.p02 was used in this work [12]. The physics list used in this study is QGSP_BIC_HP_EM4 with radioactive decay enabled. In particular, G4 EmStandardPhysics_option4 was implemented for modeling Electromagnetic process, G4 HadronElasticPhysics for elastic process of hadrons, G4 HadronPhysicsQGSP_BIC for inelastic process of hadrons, G4 RadioactiveDecayPhysics for radioactive decay, and G4 IonBinaryCascadePhysics for inelastic process. The quark-gluon string precompound (QGSP) model was implemented to handle collision of high-energy hadrons, and the binary cascade model was used for inelastic process of hadrons. The high precision data were set for the low-energy neutron and light ions. The details of the hadron interaction and ionization model in Geant4 can be found in [PERSON] et al. [13].  
Since elastic and inelastic interactions due to the nuclear reactions of radiation particles and materials are critical to predict secondary particle yields, the Joint Evaluated Fission and Fusion File (JEFF) 3.3 Nuclear Data Library was added to the neutron simulation, and the G4 TENDL data set was also added for high precision particle transportation.  
To obtain more accurate secondary yields, the nuclear decay model was enabled with the function DO_NOT_ADJUST_FINAL_STATE. This is a function in Geant4 which instructs the simulation software not to generate artificial gamma rays for the purpose of satisfying the energy and momentum conservation in some nuclear reactions. The simulation will follow the ENDF-6 libraries [14]. Moreover, the cut-off range for secondary particles was set to 0.01 nm, so that all the secondary particles can continuously slow down to an approximation range longer than 0.01 nm [15].  
The studied primary incident particles are the LANSCE broad band neutron and protons with selected energies. These particles were generated using the Geant4 general particle source (GPS). For  
Figure 1: The Los Alamos Neutron Science Center (LANSCE) broad band neutron spectrum used in this study [8].  
neutrons, a spectrum from LANSCE was converted to a probability distribution (Figure 1) and inputted to the GPS. For protons, eight monoenergetic protons of 10, 30, 50, 63, 105, 150, 200, and 230 MeV respectively were generated, and only one of the above energies was simulated at a time. In each simulation case, the number of histories was \(10^{9}\). History in the context of Monte Carlo simulation refers to a record of a primary particle from being generated to being stopped.  
All the primary particles were generated on the top of the structure and transported by the Geant4 process class with the physics list mentioned above. The secondary particle species generated due to the interactions between the primary particles and materials was recorded by the Geant4 stepping class when the particles entered the detection layer. To prevent the partial volume effect, which usually happens when the scoring volume overlaps two or more materials at the geometry boundary [16], the energy deposition was calculated by the Geant4 tracking class which sums up all the energy deposition in each step from the track passing through the detection layer. The details of the Monte Carlo technique used in this work and the associated issues can be found in a study by [PERSON] and colleagues [17].  
Since there is no method to measure the LET spectrum in an actual integrated circuit, our simulation is benchmarked with the simulation results of O'Neill for pure silicon [16], and good agreement was obtained. In fact, the same simulation setup has been used for simulating the microdosimetry property of protons and photons in biological targets with 1 \(\upmu\)m diameter and again good agreement was obtained. This work was reported by [PERSON] et al. [18].