3. Single-Event Effect Prediction Methodologies

In addition to experimental activities, the utilization of modeling and simulation has long played a vital role in investigating physical phenomena, particularly in the field of electronics, where it has been instrumental in studying the behavior of Metal-Oxide Semiconductor (MOS) transistors [1, 2]. With the increasing complexity of very-large-scale integration (VLSI) systems in each new technology generation, simulation studies have become indispensable for verifying and aiding in the development of such circuits. In this context, Monte Carlo simulation tools have emerged as a robust approach for exploring radiation effects on electronics [3]. Numerous studies in the literature have leveraged simulations to investigate radiation effects on electronics, offering an alternative to time-consuming and expensive radiation campaigns [4‐11].

In Table 3.1, a non-exhaustive list of simulation tools dedicated to model and study radiation effects on electronics is presented. Further details adopted in each tool can be found in their respective reference. In the simulations developed in this book, the MC-Oracle tool [6] is used to account for the energy deposition and charge collection in our SEE predictive methodology.

While simulation tools cannot completely replace the need for experimental data, they offer valuable insights into radiation effects by providing useful pre- and post-irradiation information. By employing modeling and simulation, researchers can gain a better understanding of the various mechanisms that occur at the circuit and component levels, thereby maximizing the outcomes of an irradiation campaign. Additionally, simulation enables the testing of hypothetical devices or conditions that may be challenging to reproduce experimentally or during an irradiation campaign.

Mixed-mode technology computer-aided design (TCAD) simulations have been vastly used to understand the main mechanisms in SEEs on electronics. However, Monte Carlo (MC) simulation codes can have a computation time several orders of magnitude lower than TCAD simulations [3, 10]. In addition, the randomness and stochastic nature of particle interaction with matter is a perfect fit for Monte Carlo (MC) simulations. Accordingly, a diverse number of models based on the MC method have been proposed to estimate and predict the radiation robustness of electronics [4‐7, 10]. Unlike deterministic models, the MC method utilizes random sampling and statistical modeling to approximate solutions for stochastic problems, such as in particle physics.

The key ingredient of SEE simulation tools is the triggering criterion, which states whether a given particle in given conditions is able to trigger an SEE. Here we present two widely used criterions: the rectangular parallelepiped (RPP) and the drift-diffusion-collection.

Circuit simulators, such as simulation program with integrated circuit emphasis (SPICE), are software tools used to solve a system of equations that fundamentally describe the basic functionality of elementary electronic components (transistors, capacitors, resistors, and diodes) within a circuit. Using the drift-diffusion-collection approach allows us to evaluate the shape and amplitude of the transient current at each electrode. These transients will depend on the nature of the ion, its LET, its location, and its direction. When studying single-event effects at the circuit level, the transient current is modeled as a parasitic current source connected to the node of the circuit where the particle hit. It is sometimes useful to use an analytical expression of the transient current, and the analytical model proposed by Messenger [24] is widely used to describe the radiation-induced current as a double exponential transient pulse: where \(t_r\) and \(t_f\) are the rising and falling time constants, respectively. These time constants correlate to the ionization track formation and the collection efficiency of the p-n junction of the injecting node [25]. Besides being technology dependent, these variables are also influenced by the relative distance of the particle hit. However, several estimation approaches have been proposed based on usually known technology parameters [24‐27]. For example, in [27], the double exponential law was verified against the circuit simulation using the transient pulse obtained from a physical model based on the diffusion of carriers. The authors conclude that the double exponential law approach can induce an overestimation of approximately 10–20% on the Single-Event Upset (SEU) cross section of SRAM cells. Additionally, it was shown that the rising time constant \(t_r\) can be simplified in the Messenger’s analytical model by considering that its value is one fifth of \(t_f\) value:

And as proposed by Messenger in [24], the \(t_f\) can be calculated based on the minority carrier mobility \(\mu \) and the substrate doping density of the p-n junction, with the following equation: where k is the Boltzmann constant, \(\epsilon _{0}\) is the permittivity of vaccum, \(\epsilon _{Si}\) is the relative permittivity of silicon, and q is the electron charge. Once these double exponential law parameters are defined, the radiation-induced current can be injected in the sensitive nodes of the circuit in a transient analysis simulation using SPICE. In Fig. 3.2, the schematic of an inverter and the corresponding current source for each type of particle hit is shown. If the particle strikes an N-channel metal-oxide semiconductor (NMOS) device, the current source is introduced between the drain of the transistor and the ground supply. Conversely, if the particle impacts a P-channel metal-oxide semiconductor (PMOS) device, the current source is connected between the drain of the transistor and the power supply. This distinction arises due to the different operating principles of NMOS and PMOS transistors, leading to different transient behaviors depending on the type of transistor affected by the radiation event.

To ensure an accurate assessment of single-event effect (SEE) immunity in digital circuits, it is highly recommended to adopt a multi-scale and multi-physics methodology that considers the complex effects at both the silicon and circuit levels [5, 14]. Various approaches have been developed, encompassing aspects ranging from particle interaction physics to circuit layout design, as discussed in [10]. As aforementioned, emerging effects such as parasitic bipolar amplification (PBA) and charge sharing effects need to be carefully addressed when analyzing radiation interaction in highly scaled technologies [7, 28, 29]. Therefore, layout information from the circuit design is an important determinant of the SEE prediction of electronic circuits. Accordingly, in this work, a layout-based methodology to assess the SEE robustness of digital circuits using the MC-Oracle prediction tool [6] is proposed. MC-Oracle is a Monte Carlo simulation code developed to analyze the SEE immunity of electronics based on the particle interaction physics within the sensitive devices. As neutrons, protons, and ions can be simulated, the circuit sensitivity can be calculated for different radiation environments such as space, atmosphere, ground, and accelerators.

As explained in Chap. 1, energetic particles when interacting with silicon go through energy loss mechanisms such as the ionization process (i.e., generation of electron-hole pairs). This energy loss is responsible for the deposition of a parasitic charge that can be collected by the sensitive transistor junctions and disturb the correct functionality of the circuit. Since neutrons are uncharged particles, they do not experience coulombic interactions with orbital electrons. Consequently, neutrons cannot ionize matter directly, howsoever, it is still considered a threat to electronics in space and aviation applications due to their indirect ionization capability [30, 31]. Considering neutrons can experience nuclear reactions with the material target nuclei, they can induce SEE through the ionization of secondary products of nuclear reactions. Also, as it presents no electromagnetic interaction, neutrons are highly penetrating particles. In the MC-Oracle, the ionization process is modeled using tables of range and electronic stopping power pre-calculated with the stopping and range of ions in matter (SRIM) code [32]. For the nuclear reactions induced by protons or neutrons, a pre-calculated nuclear database for a given energy range is built based on the detailed history of recoiling ions induced by nucleons (DHORIN) code [33]. The location of each nuclear reaction is determined considering the information from the nuclear database in which the mean free path of each particle, i.e., the average distance traveled between collisions is estimated from the nuclear cross section.

In the MC-Oracle simulation, the energy deposition resulting from ionization and nuclear reactions is modeled, followed by the simulation of charge transport and collection using the drift-diffusion mechanism. Hundreds of thousands of particle interactions are simulated, and the resulting paths of ionizing electrons and holes are numerically divided into small fragments to calculate the transport of carriers [6, 34]. To illustrate the layout-based analysis using MC-Oracle, a simplified representation is provided in Fig. 3.3.

Given a graphical design system (GDS) file of the circuit, the collecting drain area of transistors can be identified and extracted to be submitted as input to the MC-Oracle calculations. In this example, the layout design of an inverter logic gate is shown in Fig. 3.3a. The drain area of the PMOS and NMOS devices are extracted as shown in Fig. 3.3b. Then, the drift-diffusion-collection model is applied for each ion track of the event (in the case of neutron or proton interaction, one may have several ion tracks simultaneously). Considering an event with a single ion track for the sake of simplicity, Fig. 3.3c shows that the ion track is numerically divided into small fragments in which the generated charges diffuse to the collecting drain areas. Each collecting area is divided into elementary collecting areas and the induced transient current is calculated from the integration of the collected charge along the ionizing track for each elemental section of the collecting area, Fig. 3.3c. For each particle event, MC-Oracle calculates the induced transient current for each collecting area of the circuit design and stores this information in a SET current database. Therefore, multiple-node charge collection effects such as charge sharing mechanism and pulse quenching effects can be evaluated using this tool [28]. A simplified full custom design flow with the SEE characterization methodology using MC-Oracle is shown in Fig. 3.4. Given the specifications concerning the system functionality and reliability (including the radiation environment), the design engineer can start the circuit design process. Once the physical verification, i.e., design rule check (DRC), and layout versus schematic (LVS) are performed, the parasitic extraction of the netlist description and GSDII file can be obtained and submitted to the SET characterization.

The proposed SET characterization is divided into main two steps: first, aiming to build a SET current database, the MC-Oracle tool is used to perform the simulation of the particle transport and the charge collection in the collecting areas of the circuit; second, a SET analyzer is responsible for the SPICE injection campaign using the current database provided by MC-Oracle. The main inputs to the SET characterization are the technology model, radiation environment specification, layout design (GSDII), and extracted netlist description of the circuit. For the SET cross section and pulse width measurement, only the transient pulses with voltage peaks higher than half of the supply voltage are considered, but this criterion can be easily adjusted to the needs of the user. Different hardening techniques can be adopted to prevent the critical electronic systems, such as spacecrafts and avionic control systems, fail due to the occurrence of SEEs. Accordingly, the proposed predictive SET characterization methodology allows the investigation of the hardening effectiveness of radiation hardening by design (RHBD) techniques at the layout level and circuit level.

In this chapter, we provided a brief overview of the modeling and prediction of single-event effects (SEEs) in electronic circuits. The increasing computational power and availability of advanced particle physics models have led to the growing use of Monte Carlo-based software tools for studying and predicting the radiation sensitivity of circuit designs.

One commonly used approach is the rectangular parallelepiped (RPP) criterion, which makes assumptions about the sensitive volume of a device. While it has limitations, the RPP approach can provide an order of magnitude estimate of the SEE cross section and allow for the investigation of various parameters such as materials and geometry. For advanced technologies, a more accurate approach is the time-dependent drift-diffusion-collection model, which takes into account charge sharing mechanisms. In electrical simulations using tools like SPICE, the double exponential law is often used to approximate the transient pulse shape, showing reasonably good agreement with the diffusion model, but with a tendency to overestimate cross sections by 10–20%.

We also described the multi-scale and multi-physics simulation chain used in this book as the methodology for SEE prediction. This approach combines particle physics simulations from the MC-Oracle tool with electrical simulations from a SEE analyzer, providing valuable information for the characterization of SEE effects in the circuit designs studied here. Given the importance of layout design in considering SEEs and implementing radiation hardening techniques, our methodology takes into account not only the circuit description in netlist format but also layout design information obtained from the GSDII file. In Chap. 4, we will present and discuss radiation hardening techniques used to enhance the reliability of circuit designs.