# The Effect of Energy Loss Straggling on SEUs Induced by Low-Energy Protons in 28 nm FDSOI SRAMs
## 3 Results

Table 3: Energy deposited in the sensitive volume calculated with LET method. of 4.60 keV and the critical energy of 3.82 keV, respectively. The critical energy was expressed by (4), in which \(Q_{e}\) is the elementary charge and \(\varepsilon\) is the average energy of 3.6 eV demanded to generate an ionized electron-hole pair in silicon, while \(Q_{critical}\) is the equivalent critical charge to \(E_{colle\_min}\) In order to precisely evaluate the critical charge, a six-transistor memory cell model was established and calibrated according to the ST28 FDSOI PDK in TACD. Ions with threshold LET struck the drain region of an off-state inverter NMOS. The critical charge was estimated to be 0.17 fC by integrating the current flowing through the drain electrode. The energy deposited by a proton arriving at part 2 should be calibrated with the energy collection efficiency \(\delta\) to judge whether it can trigger a SEU or not. \[\delta=\frac{E_{colle\_min}}{E_{dpo\_min}} \tag{3}\]  
\[E_{colle\_min}=\frac{Q_{critical}}{Q_{e}}\times\varepsilon \tag{4}\]  
Figure 6 illustrates results obtained from Geant4. The cumulative events number is the statistics of protons that deposited a given energy or greater in the sensitive volume. Incredibly, the energy deposited was broadened to about 10 keV, far beyond the estimated value based on LET, which will be exhaustively explained in the following paper. Protons at 0.9 MeV and 0.92 MeV tended to loss more energy in silicon, ascribing to that the Bragg peak reached the sensitive volume. This sharp peak below 1 MeV confirmed the experimental results documented by [5; 16; 17]. \(E_{dpo\_min}\) is also presented in Figure 6 as a vertical dashed line and Table 5 shows corresponding SEU cross-sections for each energy point. Figure 5: The divided sensitive volume. Figure 6: Geant4 simulation results. The cumulative number of protons that deposited a given energy or greater in the sensitive volume for various initial energy of the proton beam. It seems that the simulation results in Table 5 were higher than these experimental results illustrated by Table 4. Some reasons may be attributable to the difference. When a proton penetrates through the sensitive volume, excited electrons along its track may diffuse to other insensitive areas before they are collected [18]. However, they were included in our simulation. The phenomenon is especially apparent for protons that arrive at the edge of the sensitive volume. On the other hand, simulation tools of Geant4 and TCAD used in this manuscript cannot fit each other perfectly at the present stage. They both have limitations when being used to research charge generation and collection for modern SOI devices. Consequently, further work should concentrate on organically combining the two simulation tools. The distinction between simulation results and experimental results is not critical, because the main aim of this article is to point out that energy loss straggling should not be ignored any more when predicting SEUs induced by protons for circuits manufactured with SOI technology, instead of proposing an evaluation method of calculating soft error rates. Generally speaking, summarizing these results described above, it is reasonable to conclude that SEUs induced by low-energy proton direct ionization in the irradiation experiments are ascribed to energy loss straggling.