# Lineal Energy of Proton in Silicon by a Microdosimetry Simulation
## 1 Introduction  
Radiations exist around us in the air, and it includes photon, electron, neutron and alpha particle. These radiations are critical traditionally in the aerospace applications because they could render function loss for the satellites and even lead to material degradation [1], and they can be ignored at the sea level. However, as microelectronic devices are scaling down aggressively with the advancement in semiconductor technology, nano-meter devices are now susceptible to these radiations, and they can no longer be overlooked. These radiations can interact with semiconductor devices and cause damages to the devices or functional errors to their associated circuits [2]. The effect of these radiations on microelectronic devices can be categorized into two different effects, namely a cumulative effect termed as Total Ionization Dose (TID) effect, and a stochastic effect, termed as Single Event Effect (SEE) [3]. SEE describes the event of electronic device malfunction or failure caused by \"single\" radiation hits. SEE is critical for devices where their rebooting is difficult or even impossible, and examples of such devices are pacemakers, autopilot systems, and microelectronics used in space missions. Lineal Energy Transfer (LET) is widely used as a key index for SEE prediction [4, 5]. LET is a non-stochastic quantity which gave an expectation value of energy imparted from particle to a local site. International Commission on Radiation Units and Measurements (ICRU) gave the definition of LET of a particle (Equation (1)) in its report 16 [6] as the quotient of \(dE\) by \(dl\), where dl is the distance traversed by this particle and \(dE\) is the mean energy-loss owing to collisions with energy transfers less than some upper limit \(\Delta\), which is the cut off energy of delta ray. \[L_{\Delta}=\left(\frac{dE}{dl}\right)_{\Delta} \tag{1}\]  
There is a long history of studies on LET in microelectronic applications. [PERSON] et al. conducted a series of studies on LET with secondary ions generated by the irradiation of silicon with protons, and they showed that proton testing is suitable to screen microelectronic devices for low earth orbit susceptibility to heavy ions [7]. [PERSON] et al. provided the LET spectra of protons in 50-500 MeV, which are commonly used for SEE testing, and gave the scaled factor of proton fluence for Geosynchronous orbits by a simplified Monte Carlo simulation [8]. [PERSON] and [PERSON] carried out a comprehensive study of the ion ranges and stopping powers in solids and provide a useful toolkit called Stopping and Range of Ions in Matter (SRIM). This toolkit allows the radiation particles to be modelled in a simple microelectronic structure [9; 10]. [PERSON] et al. provided the trend of LET thresholds of SEE with feature sizes from 1 to 0.1 \(\upmu\)m [11]. In their results, the threshold decreases when the feature size decreases due to the following. Firstly, when the sizes of the devices are smaller, the critical charges, i.e., the amount of charges to change the performance of the devices will be smaller. Secondly, with a smaller target, the energy deposition of each specific radiation particle will have a greater deviation, and there is a chance of a huge energy deposition leading to a huge induced charge. Single Event Rate (SER) can be directly tested under specific protocols [12] or modelled with known natural radiation environment for these cosmic rays [13]. JEDEC Solid State Technology Association give the protocol JESD57A [12] to guide the procedures for the SEE tests. These tests are usually expensive and difficult. Another way to predict single event rate is to convolute the LET spectra in target orbital with the single event cross sections (either for a device or averaged per bit) from either experiment or simulation. In this method, single event cross sections versus LET is usually a single value function.