# New SEU modeling method for calibrating target system to multiple radiation particles

Pablo Caron, Christophe Inguimbert, Laurent Artola, Françoise Bezerra, Robert Ecoffet

► To cite this version:

Pablo Caron, Christophe Inguimbert, Laurent Artola, Françoise Bezerra, Robert Ecoffet. New SEU modeling method for calibrating target system to multiple radiation particles. IEEE Transactions on Nuclear Science, 2019, 67 (1), pp.44 - 49. 10.1109/TNS.2019.2953995. doi:10.1109/TNS.2019.2953995

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Distributed under a Creative Commons Attribution 4.0 International License
New SEU Modeling Method for Calibrating Target
System to Multiple Radiation Particles

P. Caron<sup>B</sup>, C. Inguimbert, L. Artola<sup>B</sup>, F. Bezerra, and R. Ecoffet

***Abstract***—This article proposes a method using electron and proton Single Event Upset sensitivities of a device to deduce all simulation parameters related to an RPP approach. It is shown that for 45-nm double data rate (DDR) memory, the RPP approach is still relevant and the crossing of proton and electron data makes it possible to constrain and properly define the associated parameters. Heavy ion prediction is also presented.

***Index Terms***—Double data rate synchronous dynamic random access memory (DDR SRAM), electron-induced single event upset (SEU), heavy ion-induced SEU, proton-induced SEU, SEU.

# I. INTRODUCTION

FOR years, in the Single Event Upset (SEU) prediction domain, there were some attempts to define a bridge between the sensitivity of the devices and different kinds of particles [1]–[6]. Such methods could be used to reduce the number of experimental tests conducted during the space qualification of the device. An accurate extrapolation of the sensitivity from a particle to another particle (from protons to heavy ions, for instance) also improves the reliability of SEU rate risk assessment. Historically, methods have been proposed between protons and heavy ions. SEU cross sections can be predicted for protons, knowing the heavy ion SEU sensitivity as a function of Linear Energy Transfer (LET). However, the sensitivity of new generations of devices to both electrons [7]–[13] and protons [14]–[17] offers some new opportunities. In particular, it would allow one to accurately define the SEU critical energy and the typical dimensions of the sensitive region. Moreover, with this combined experimental data, the target system can be accurately specified and a correlation between protons, electrons, and heavy ions is established. The purpose of this article is to take advantage of increasing sensitivities of integrated devices to various particles to develop a simple predicting method based on the rectangular parallelepiped (RPP) approximation.

The goal of this study is to improve the accuracy of establishing the key parameters used in this prediction approach

(e.g., RPP-sensitive volume and critical energy), and thus the overall accuracy of this rate prediction approach.

By analyzing each of the contributions (physical processes) leading to an upset and using experimental measurements of SEU sensitivity of a device, a method to calibrate all the sensitive parameters is proposed. A dedicated GEANT4 [18], [19] application has been developed to implement this method. The MicroElec [20], [21] module has been used to simulate the full ionization cascade.

This article is divided into two parts. First, the procedure used to determine the parameters of the target system is explained. Then, in a second step, the proposed method was applied to a device having a large data set involving electron, proton, and heavy ion data. This is the Renesas double data rate synchronous dynamic random access memory (DDR SRAM) [22].

# II. RPP APPROXIMATION

For modeling SEUs, it is common to approximate the sensitive region of a device using a parallelepiped and the critical energy [23], [24]. This approximation results in four unknowns: 1) the overlayer compositions/thicknesses; 2) the critical energy; and 3) the sensitive volume, which could be decomposed into a sensitive thickness and a sensitive surface.

The critical energy is the criterion for triggering an upset. If the deposited energy in the sensitive volume is greater than the critical energy, then an upset occurs. The difficulty of this approach is that the definition of each of these parameters is a priori dependent on each other. Indeed, different parameter sets can be a solution to this system. Based on electron and proton experimental data, the method presented here allows one to strongly constrain the four unknowns of the system to find the best set of parameters to describe the device.

# III. NEW METHOD

## A. Proton Data

Fig. 1 presents the typical SEU behavior of a device under proton irradiation. Some information can be directly interpreted with this data [25].

1) *Magnitude of the Ionization Peak*: At low incident proton energy, the peak is attributed to direct proton ionization. The magnitude of this peak is correlated with the critical energy and the sensitive volume. However, as a first approximation, the deposited energy can be considered as proportional to the

P. Caron, C. Inguimbert, and L. Artola are with ONERA-DPHY, 31055 Toulouse, France (e-mail: pablo.caron@onera.fr; christophe.inguimbert@onera.fr; laurent.artola@onera.fr).

F. Bezerra and R. Ecoffet are with CNES, 31401 Toulouse, France (e-mail: francoise.bezerra@cnes.fr; robert.ecoffet@cnes.fr).
<figure><img src="image_2.png" /><figcaption>Fig. 1. Proton-induced SEU cross sections based on the experimental data for [22]. Some information can be extracted and interpreted. The dashed lines are indicators about the different parts of SEU sensitivity curves.</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Fig. 2. Electron-induced SEU cross sections based on the experimental data for [22]. Some information can be extracted and interpreted. The dashed lines are indicators about different parts of the SEU sensitivity curves.</figcaption></figure>

sensitive thickness, making the energy deposition under normal incidence beam mainly driven by the sensitive thickness. Therefore, there is a strong dependence between the maximum of the ionization peak, the critical energy, and the sensitive thickness.

2) *Position of the Ionization Peak*: Before reaching the sensitive volume, the incident protons must cross the overlayers. When the incident energy is too low, the incident protons do not reach sensitive volumes causing the sensitivity to fall rapidly down to zero. The worst case in terms of SEU is when protons are strongly slowed down by overlayers and reach sensitive volumes with energy close to the critical energy of the device. Thus, the position (energy) of the ionization peak is strongly correlated with the composition/thickness of the overlayers.

3) *Nuclear Reaction-Saturated Response Curve*: At high energy values, SEUs are mainly induced by nuclear reactions. At very high energies, where the SEU cross sections become saturated, the amount of SEU can be considered to be proportional to the number of nuclear reactions produced in the sensitive volume. The saturation level is thus mainly correlated with the sensitive volume. However, it is impossible here to deduce the surface and the thickness from the volume. However, by coupling this information with the Magnitude of the ionization peak, it will be possible to calibrate the sensitive surface area and the sensitive thickness of the device.

4) *Transitional Part*: Some articles show that the Coulomb elastic scattering process can contribute mainly to the device sensitivity in this region of energy [10], [11], [26]. Thus, when the Coulomb elastic contribution appears and makes the transition between ionization and nuclear contributions, it is possible to deduce information about the critical energy and the sensitive volume.

## B. Electron Data

Fig. 2 presents the typical SEU behavior of a device under electron irradiation.

1) *Energy Threshold*: The first measurements (in terms of energy) of SEU under electrons are particularly interesting because these data establish the critical energy of the device. In recent articles, we have discussed the sensitivity of the devices to electrons [10], [11]. Different physical processes are involved within the sensitivity to electrons (e-/nucleus Coulomb scattering, electronuclear processes, inelastic e-/e-scattering). Depending on the critical energy, the contribution to the SEU cross sections of these mechanisms can be different.

2) *Nuclear Reaction-Saturated Response Curve*: As with protons, this part is mainly driven by the sensitive volume. Indeed, analogous to protons, the number of events induced by nuclear (elastic and/or inelastic) interactions is proportional to the volume of the sensitive regions. It is not possible to deduce directly the sensitive surface area and the thickness from this information. But, by coupling this information with the Magnitude of the ionization peak of the protons, it will be possible to calibrate the sensitive surface area and the sensitive thickness, and also to make a cross comparison with proton data.

## IV. APPLICATION: PARAMETER EXTRACTION

As presented in Section III, by analyzing the different contributions (ionization process, Coulomb elastic scattering, and nuclear reactions) involved in electron and proton environments, it is possible to link these physical mechanisms to RPP parameters. The measurements on the Renesas device [22] are particularly convenient because a large number of data on different energy ranges are provided, making it possible to identify different SEU regimes (ionization peak, transitional part, nuclear saturation level...). To perform an example using the method presented here, it is necessary to have experimental data for the same device under proton and electron irradiation. The Renesas device tested by Sukhaseum et al. [22] responds to these criteria.

GEANT4 [18], [19] has been used to develop an RPP SEU prediction application capable of accurately modeling the
ionizing deposited energy using incoming electrons, protons, and heavy ions. The MicroElec module [20], [21] was used to simulate the transport of these particles down to low energies (down to 16.7 eV for electrons, which allows one to correctly track the secondary electrons, and thus check if they leave the sensitive volume). The case of Renesas DDR SRAM 45 nm has been treated. The best set of RPP parameters has been estimated.

The initial RPP parameters are to be defined. Random RPP parameters could be chosen, but to optimize the approach, RPP parameters can be found in the literature for equivalent devices (technological node, technological architecture...). A first set of RPP parameters has been defined as follows.

- Overlayer thickness: 10 µm.

- Sensitive volume : a 500-nm sided parallelepiped.

- Critical energy: 30 keV.

Based on these initial RPP parameters, the overlayer characteristics are first extracted from the position of the ionization peak. We assume that these overlayers are a simple silicon block. Protons with energies between 0.2 and 1 MeV (in accordance with the experimental ionization peak) are sent at normal incidence to the overlayers and the deposited energies in the sensitive volume are recorded. As explained in [25], by playing with the thickness of the overlayers, the position of the ionization peak is shifted. Only the position of the peak is searched in this step. A dichotomy procedure is then used: the variable to be adjusted is the thickness of the overlayers. When the simulated ionization peak is adjusted as well as possible, in the least-squares sense, a value of the thickness of the overlayers is obtained. This value will no longer need to be modified later.

Then, the volume $V = S \cdot h$ ($S$ is the sensitive surface area and $h$ the sensitive thickness) is extracted from the saturated level of the electron-induced and proton-induced SEU (in this first step, it is assumed that nuclear reactions systematically trigger an upset).

The critical energy can be limited by the distribution of the recoil energies of the electronuclear reactions and the magnitude of the proton SEU cross sections induced by Coulomb elastic contribution. Then, the critical energy and the sensitive thickness are adjusted, so that the simulated ionization peak follows the experimental ionization peak by keeping $V$ fixed. To do this, as for determining the thickness of the overlayers, protons with energies between 0.2 and 1 MeV are sent at normal incidence to the overlayers. The experimental values of the associated SEU cross sections are expected to be reproduced.

The procedure is repeated without making the assumption of triggering an upset at each nuclear reaction, but using the critical energy deduced. The sensitive volume $V$ is therefore subject to change. The total procedure is repeated in order to be as close as possible, in the least-squares sense, to all of the experimental measurements.

### A. Renesas DDR SRAM 45-nm

The analysis started with input parameters in accordance with the device technology considered: a sensitive

<figure><img src="image_4.png" /><figcaption>Fig. 3. Data presented in Figs. 1 and 2 are reproduced here with our simulation results when the best set of parameters are found. Blue triangles and associated simulated results correspond to the proton data. Orange squares and associated simulated results correspond to the electron data.</figcaption></figure>

volume of 500 × 500 × 500 nm³, a critical energy of 30 keV, and an overlayer thickness of 10 µm [8], [12]. After applying the method detailed in the previous section, the following parameters were obtained: a sensitive volume of 800 × 800 × 400 nm³, a critical energy of 45 keV, and an overlayer thickness of 8 µm. Fig. 3 presents the results obtained with these parameters. Several things should be noted. First, the dynamics of the SEU sensitivity of the device are very well reproduced (for both protons and electrons). Of course, we could say that this is obvious since the parameters are adjusted to do so. But let us remember that the same set of parameters is used, whether in an electron or a proton environment. It is this last point that is particularly interesting. Second, since our parameters are consistent for both electron and proton data, the simulation results derived are more reliable. Finally, it should be noted that, unlike our previous work [10], [11], the SEU measurements induced by electrons between 10 and 30 MeV are explained, for the Renesas device, by the electronuclear reactions. Indeed, the contribution of the elastic Coulomb interactions, in the case of the Renesas device, starts for higher incident electron energies than for the Spartan-6 device. This is simply due to the critical energy associated with these memories. As the critical energy of the Spartan-6 device was lower (about 10 keV), the Coulomb elastic contribution started at lower energies.

Since the parameters have been deduced and seem to reproduce very closely the sensitive regions of the device, an investigation was carried out on the possibility of predicting the sensitivity of this device for another kind of environment.

## V. APPLICATION: HEAVY ION SENSITIVITY PREDICTION

### A. Presentation of the Model

In addition to electron and proton data, the Renesas device has also been irradiated with heavy ions [22]. Fig. 4 presents the SEU cross sections of the Renesas device under heavy-ion irradiation. A proton SEU cross section has been added, associated with the maximum of the ionization peak and corresponding to 0.5 MeV·cm²/mg.
<figure><img src="image_5.png" /><figcaption>Fig. 4. Renesas SEU induced by heavy-ions [22] (blue triangles). Proton data corresponding to the 0.5 MeV cm²/mg case is added (red square).</figcaption></figure>

According to the parameters defined during the previous calibration, it is now possible to perform prediction concerning heavy-ion sensitivity. To do that, a relatively simple model has been adopted. This model is based on (1) [27]–[30]. The main idea of this model is to link the event multiplicity with the LET. This model mainly concerns integrated devices (with feature sizes less than 100 nm, as mentioned by Zebrev and Zemtsov [29]), and (1) is appropriate for LETs that do not allow the saturation level to be reached (see Fig. 4).

$$ \sigma(\Lambda) = \frac{S \cdot \rho_{\text{Si}}}{E_c} \cdot t_{\text{eff}} \cdot \Lambda \quad (1) $$

where $t_{\text{eff}}$ is the effective collection length, $\rho_{\text{Si}}$ is the silicon mass density (~2.32g/cm³), $\Lambda$ is the LET, and S and $E_c$ are, respectively, the sensitive surface area and the critical energy associated with the device. This expression shows the linear dependence of the SEU cross sections as a function of the LET since all the parameters mentioned are assumed to be independent of the LET.

In Section IV, all RPP parameters of the Renesas device were evaluated. The sensitive surface area was determined as 800 × 800 = 0.64 µm² and the critical energy was found to be equal to 45 keV. Nevertheless, $t_{\text{eff}}$ is device-dependent or, at least, technology-dependent (bulk versus silicon on insulator (SOI), for instance).

Another important point addressed in [29] is the recombination effect. As can be seen in Fig. 4, very high LETs were used (up to 60 MeV cm²/mg). With such values, it is necessary to take into account the recombination effect. The same question is legitimate concerning recoil elements generated during nuclear reactions induced by incident protons and electrons. GEANT4 simulations about energy distributions were performed to solve this problem. Fig. 5 focuses on the case of silicon recoil elements in the silicon material. It appears that in the worst case (proton inelastic nuclear reactions), the mean energy of the silicon nuclei generated is about 1.5 MeV, which corresponds to a LET of 6.5 MeV cm²/mg.

Knowing the LETs involved either directly (Fig. 4) or indirectly (Fig. 5), it is now necessary to take into account the recombination effect as a function of LET. For this, the model of [29] was used

$$ \eta_{\text{eff}}(\Lambda) = 1 - f_A \cdot \eta_{\text{eff}}^3. \quad (2) $$

<figure><img src="image_6.png" /><figcaption>Fig. 5. GEANT4 simulation results of the mean silicon energy generated by nuclear reactions as a function of incident energy in the silicon target.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Fig. 6. Charge yield efficiency as a function of the LET.</figcaption></figure>

Here, $\eta_{\text{eff}}$ is an effective charge yield and $f_A = (\Lambda/\Lambda_{\text{Auger}})^2$ where $\Lambda_{\text{Auger}}$ takes into account the Auger recombination. Zebrev and Zemtsov [29] analyzed two devices with different technologies, 90-nm bulk and 45-nm SOI. Very different values of $\Lambda_{\text{Auger}}$ are identified to reproduce the behavior of these devices. Fig. 6 presents the calculation of $\eta_{\text{eff}}$ for these two cases.

These two values of $\Lambda_{\text{Auger}}$ generate large differences in the evolution of $\eta_{\text{eff}}$ as a function of LET. Nevertheless, below 5 MeV·cm²/mg, the calculated efficiencies are near 1. Thus, in a first approximation, the SEU saturation levels reached by electronuclear and protonuclear processes can be considered as undisturbed by the recombination effect. This is not the case for experimental data obtained with incident heavy ions that have high LET for which the recombination process can drastically reduce the charge that can effectively participate in the triggering of upset. Thus, during heavy-ion simulations, it is necessary to take into account this effect.

## B. Extraction of Parameters

As the sensitive surface area ($S = 800 \times 800 = 0.64 \ \mu\text{m}^2$) and the critical energy ($E_c = 45$ keV) are determined with the method presented previously, the calculation of (1) now
<figure><img src="image_8.png" /><figcaption>Fig. 7. Experimental data provided by Gadlage *et al.* [12] (bulk 45-nm). $S \sim 0.12 \ \mu\text{m}^2$ and $E_c = 10$ keV are calculated in [11]. $t_{\text{eff}} = 6$ nm is applied to obtain the blue curve.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 8. Experimental data provided by Sierawski *et al.* [14] (bulk 65-nm). $S \sim 0.25 \ \mu\text{m}^2$ and $E_c = 22$ keV are calculated in [25]. $t_{\text{eff}} = 6$ nm is applied to obtain the blue curve. $\Lambda_{\text{Auger}} = 54$ MeV cm$^2$/mg is applied to obtain the orange curve.</figcaption></figure>

depends on only one variable: $t_{\text{eff}}$. The calculation of (2) also depends on only one unknown: $\Lambda_{\text{Auger}}$. As these two parameters were not already evaluated for the Renesas device, we have evaluated them for other devices. As will be seen later, it would seem that for bulk devices, the values of $t_{\text{eff}}$ and $\Lambda_{\text{Auger}}$ do not change much from one manufacturer (Renesas versus Xilinx, for instance) to another. Thus, to extract these two parameters, an investigation about bulk devices was carried out. These equivalent devices, the 45-nm Spartan-6 and the 65-nm TI device, have already been analyzed in previous work [11], [25]. They were irradiated under heavy ions and SEU measurements are available [12], [14]. The sensitive surface area $S$ and the critical energy $E_c$ have been already estimated in [11] and [25]. Thus, by using (1) and (2) to reproduce the experimental measurements, only the $t_{\text{eff}}$ and $\Lambda_{\text{Auger}}$ parameters need to be adjusted. Figs. 7 and 8 present the heavy-ion-induced SEU cross section experimental data and our simulated results, once $t_{\text{eff}}$ and $\Lambda_{\text{Auger}}$ have been adjusted. It is particularly interesting to note that for these two devices, the same $t_{\text{eff}}$ (6 nm) was applied to fit the experimental data. The last device exhibits recombination effects due to the high LET applied. In order to better match with the experimental

<table><caption>TABLE I
EXTRACTED PARAMETERS OF THE ZEBREV *et al.* MODELS</caption><tr><td>This work</td><td>6</td><td>54</td></tr></table>

Note that the impact of the Auger recombination considered for the bulk devices studied here ($\Lambda_{\text{Auger}} = 54$ MeV·cm$^2$/mg) is the smaller of the two cases presented in Fig. 6. Thus, for low-LET, the effect of recombination does not significantly influence heavy-ion-induced SEU measurements (as seen in Figs. 7, 8 and 9).

<figure><img src="image_10.png" /><figcaption>Fig. 9. Heavy ion-induced SEU cross sections for the Renesas device.</figcaption></figure>

data, the value of $\Lambda_{\text{Auger}}$ (54 MeV·cm$^2$/mg) recommended by Zebrev and Zemtsov [29] for a bulk 90-nm device has been used. So, for two bulk devices of different integration levels (90 nm vs. 65 nm), the same value of $\Lambda_{\text{Auger}}$ is found. Thus, as mentioned at the beginning of this section, for bulk devices, it would appear that $t_{\text{eff}}$ and $\Lambda_{\text{Auger}}$ parameters are not very dependent on the integration levels (90, 65, and 45 nm) and the device manufacturers (Renesas, TI, Xilinx).

This set of parameters, listed in Table I, will be used to study the SEU sensitivity of the Renesas device under heavy-ion irradiation.

### C. Renesas 45-nm Device

All the parameters of the models are determined. Fig. 9 presents our heavy-ion-induced SEU prediction on the Renesas device, based on the sensitive volume and the critical energy calibrated with the electron and proton data (Fig. 3). A good agreement is found between our prediction and experimental data. The importance of taking into account the recombination effect can be noticed. Otherwise, the deduced SEU cross sections may be overestimated (blue curve).

## VI. CONCLUSION

This article presents a method to investigate the SEU sensitivity of memory devices. In the RPP approximation, it is demonstrated that a single set of parameters defining the device within the RPP approximation can be defined
for incident electrons, protons, and heavy ions. Both the geometric parameters (sensitive area and sensitive thickness) and the critical energy can be common to both electron and proton irradiation. The cross-analysis of electron and proton sensitivity allows finding the best set of parameters for calibrating the sensitive regions of the tested device. A dedicated GEANT4 application has been developed to automatically adjust the RPP parameters and handle the constraints imposed by the experimental measurements. Using the parameters so defined, the heavy ion sensitivity prediction is found to be in good agreement with experimental data according to the model of Zebrev *et al*. But good prediction requires the use of a charge recombination model and the consideration of the triggering of multiple events. To do so, simple models were used. To define the intrinsic parameters of these models, a study conducted on equivalent devices (bulk technology) to the Renesas device was carried out. Similarities were found in the values of these parameters. It should, however, be noted that this preliminary study was necessary to investigate the case of the Renesas device. Nevertheless, a database of these parameters could be created from all the SEU measurements available in the literature. Our conclusions on the low dependence of these parameters according to the integration levels could be then validated. In addition, a strong dependence of these parameters with the technological architecture (bulk, SOI, ...) is expected. This would therefore extend the predictive capacity of the approach proposed in this article.

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