# The Effect of Energy Loss Straggling on SEUs Induced by Low-Energy Protons in 28 nm FDSOI SRAMs
## 3 Results  
Under the circumstance of energy loss straggling being ignored, SEUs should not have been observed during exposure. The possibility of nuclear reactions between low-energy protons and other atoms in devices is extremely low, therefore upsetting observed in experiments were actually caused by proton direct ionization. According to the method based on LET, energy deposited in sensitive volume referred to the 22 nm thick drain region can be calculated by (1) and the results are presented in Table 3. In Formula (1), \(P_{LET}\) and \(\Delta\)X represent the LET of proton in silicon and the trajectory length of an incident particle, respectively, whereas \(\rho_{Si}\) is the density of silicon. It is worth noting that protons with different energy correspond to different LET values according to SRIM calculation. \[\mathrm{E}=P_{LET}\times\Delta X\times\rho_{Si} \tag{1}\]  
The minimum depositing energy \(E_{depo\_min}\) required to trigger SEUs could also be calculated by (1), which was 4.60 keV. It was considerably larger than the results shown in Table 3. The supply voltage of SRAMs was observed to modestly descend to 0.8 V on account of TID effects during performing experiments. And a relevant prediction of 0.9 MeV-cm\({}^{2}\)/mg for the threshold LET was made by technology computer aided design (TCAD) simulation. Thus, the value \(P_{LET}\) should be 0.9 MeV-cm\({}^{2}\)/mg here. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Proton Energy [MeV]** & **Incident Direction** & **Proton Number** \\ \hline
0.90 & Vertical & \(5\times 10^{6}\) \\ \hline
0.92 & Vertical & \(5\times 10^{6}\) \\ \hline
2 & Vertical & \(5\times 10^{6}\) \\ \hline
3 & Vertical & \(5\times 10^{6}\) \\ \hline
5 & Vertical & \(5\times 10^{6}\) \\ \hline
8 & Vertical & \(5\times 10^{6}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation Setup. Figure 3: (**a**) The top view of the memory cell model established in Geant4; (**b**) The front view of the Geant4 model. However, SEUs induced by protons with initial energy ranging from 2 MeV to 8 MeV indeed existed, as showed in Table 4. The cross-sections of each energy point were calculated by (3) and relevant results were given in Figure 4. In Formula (3), \(N_{\textit{insets}}\) represents the number of upsets recorded by the monitor computer while \(F_{\textit{proton}}\) and \(V_{\textit{SRAM}}\) represent particle fluence and memory capacity, respectively. Since multiple-bit upsets (MBUs) were hardly observed during exposure, black circles are virtually regarded as single-bit upsets (SBUs). \[\text{Cross - Section}=\frac{N_{\textit{upsets}}}{F_{\textit{proton}} \times V_{\textit{SRAM}}} \tag{2}\]  
There is a variation of energy collection efficiency in different regions of the sensitive volume [3]. Consequently, this factor should be taken into consideration to more accurately evaluate SEU cross-sections. The sensitive volume was divided into three parts according to [3], as shown in Figure 5. Part 1 and part 3 corresponded to quite low energy collection efficiency of 10% which could be ignored, whereas part 2 occupying about half of the area corresponded to a high value. The value was calculated by (3). In this equation, \(E_{\textit{drop\_min}}\) and \(E_{\textit{colle\_min}}\) represent the minimum depositing energy \begin{table}
\begin{tabular}{c c c} \hline \hline
**Proton Energy [MeV]** & **Upsets** & **Cross-Section [cm2/bit]** \\ \hline
2 & 7 & \(6.70\times 10^{-17}\) \\ \hline
3 & 9 & \(1.40\times 10^{-16}\) \\ \hline
5 & 6 & \(1.25\times 10^{-16}\) \\ \hline
8 & 44 & \(8.26\times 10^{-17}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Experimental SEU results. Figure 4: SEU cross-sections at each energy point. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Proton Energy [MeV]** & **LET in Silicon [MeV-cm2/mg]** & **Energy Deposited [eV]** \\ \hline
2 & 0.1124 & 573.99 \\ \hline
3 & 0.0849 & 433.55 \\ \hline
5 & 0.0587 & 299.76 \\ \hline
8 & 0.0413 & 210.90 \\ \hline \hline \end{tabular}
\end{table}