# The Effect of Energy Loss Straggling on SEUs Induced by Low-Energy Protons in 28 nm FDSOI SRAMs
## 4 Discussion  
Last section illustrated that energy loss straggling contributed significantly to the SEUs observed during exposure. To make further interpretation, an auxiliary experiment was performed in Geant4. Two silicon detectors were established, of which one was 1 \(\upmu\)m thick according to the charge collection depth for nanometer CMOS bulk technologies [19] and the other was 22 nm thick corresponding to the sensitive volume of ST28 FDSOI technology. Further, 10,000 monoenergetic protons at 1.5 MeV struck each silicon detector vertically. The statistical results of deposited energy are illustrated by Figure 7, in which the frequency represents the possibility of energy lost by a proton falling into a given interval. Compared with a symmetrical less broadened energy spectrum for the 1 \(\upmu\)m thick detector, an extremely broadened curve was obtained for the 22 nm thick one. Our results were consisted with the discovery made by previous researchers that energy loss distribution for charged particles in thin matter was similar with the Landau distribution [20]. It is worth noting that there should have been a peak in the curve presented by Figure 7b, but the peak was extraordinary narrow that it actually fell into a given energy interval. \begin{table}
\begin{tabular}{c c c} \hline
**Proton Energy [MeV]** & **Upsets** & **Cross-Section [cm\({}^{2}\)/bit]** \\ \hline
0.9 & 95 & \(3.65\times 10^{-13}\) \\ \hline
0.92 & 100 & \(3.85\times 10^{-13}\) \\ \hline
2 & 7 & \(2.69\times 10^{-14}\) \\ \hline
3 & 15 & \(5.77\times 10^{-14}\) \\ \hline
5 & 14 & \(5.38\times 10^{-14}\) \\ \hline
8 & 10 & \(3.85\times 10^{-14}\) \\ \hline \end{tabular}
\end{table} 
Table 5: Simulation results of single event upset (SEU) cross-sections. This phenomenon can be explained by the statistical fluctuation referring to the number of collision events between protons and extranuclear electrons of silicon. As shown in Figure 8, a proton with normal incidence changes its state in terms of energy and velocity when encountering an electron. However, the final state of this proton has significant uncertainty as electrons with different kinetic energy disorderly distribute in silicon. Therefore, the distance between two collision events presents a certain randomness. This is immaterial under the circumstance of thick matter being used because a long path length for ionized particles guarantees enough collision events and energy deposited can be expressed by a mean value. By contrast, the randomness in distance means that an incident proton randomly deposits energy in ultra-thin sensitive volume, conducting in a largely broadened energy loss spectrum. Conventionally, the threshold LET is an important indicator to measure the performance of circuits which adopt radiation hardened by design (RHBD) techniques. This is based on the presumption that energy lost by monoenergetic particles in traversed material is essentially identical. But according to our Geant4 simulation, energy loss straggling is so apparent that it is unreasonable to choose a mean value to represent the ionization energy loss of protons for the 28 nm FDSOI SRAM. In other words, a proton may deposit enough energy in silicon due to energy loss straggling, although its LET calculated by SRIM is quite low. The threshold LET may not be a reliable indicator to judge whether SEUs can be triggered by given particles or not anymore. Thus, we speculate that the previous presumption can cause an underestimation in terms of the influence of low-energy protons on SEUs for modern SOI devices. This speculation is also proved by our experiments. For instance, the actually supply voltage of SRAMs modestly descended to 0.8 V  
Figure 8: The schematic diagram of collisions between protons and extranuclear electrons of silicon. Figure 7: (**a**) Energy loss spectrum for ten thousand protons penetrating through the 1 μm thick silicon detector; (**b**) Energy loss spectrum for ten thousand protons penetrating through the 22 nm thick silicon detector.