Analytical modeling of charge collection is essential for predicting single-event effects in integrated circuits subjected to radiation. This work proposes a unified model of charge collection by diffusion in semiconductors in one, two, and three dimensions, accounting for recombination effects. We derive exact expressions for the carrier density, diffusion current, and collected charge using the solution of the diffusion equation for a point source. We formulate the collected charge using Bessel functions, which allow for a more general and fully analytical description of the problem. The model emphasizes the role of geometry by explicitly accounting for the dimensionality of the problem. It also establishes that, for any dimension, the collected current peaks before the carrier density does. We also propose analytical expressions for the collection efficiency and the recombination factor, with simplified forms in the absence of recombination. A minimal Python implementation is provided to facilitate the practical application of the model. Finally, we outline how to use the proposed model to perform realistic simulations of single events and relate the results to the soft error rate of a given device.

The present study investigates the effects of neutron shielding by concrete slabs in the context of nuclear fusion (14 MeV neutrons). MCNP and Geant4 numerical simulations have been performed to characterize neutron transport through concrete slabs with thicknesses ranging from 1 to 160 cm. Using a monoenergetic, normally incident 14 MeV neutron source, we examine neutron-flux attenuation and spectral evolution after propagation through concrete. The results show that multiple elastic and inelastic scattering processes dominate the transport, leading to a strong spectral redistribution and a significant build-up of scattered neutrons. For intermediate thicknesses (50–100 cm), the transmitted flux is largely composed of scattered and secondary neutrons, with a pronounced epithermal slowing-down component approximately following a 1/E behavior, a thermal peak resulting from hydrogen moderation, and a residual high-energy tail corresponding to partially degraded primary neutrons. At larger thicknesses (≥100 cm), absorption and capture of thermalized neutrons become dominant, resulting in a sharp decrease in the transmitted flux. The impact of these spectral modifications on the soft-error rate (SER) of microelectronic devices is evaluated by folding the transmitted neutron spectra with energy-dependent single-event upset (SEU) cross-sections representative of advanced semiconductor technologies. The results indicate that, although total neutron flux decreases significantly with increasing concrete thickness, the spectral redistribution and the persistence of intermediate-energy neutrons can maintain a non-negligible contribution to SER in certain configurations. These findings highlight the importance of using full transport simulations, including spectral effects, when assessing radiation-induced reliability risks in fusion facilities.

We performed soft error rate (SER) characterization of 40-and 65-nm bulk CMOS static random access memories (SRAMs) combined with neutron spectrometry in the deuterium-tritium (D-T)-fueled Joint European Torus (JET) tokamak during its final D-T plasma operation (September and October 2023) producing a series of several dozens of power pulses. Our experimental results demonstrate the impact of machine operation on the electronics' reliability, emulating realistic conditions for circuits exposed to the partially radiation-shielded environment of future fusion reactors. Typical bit-flip (BF) rates of 493 h(-1)Gbit(-1) for 65-nm SRAMs and 2342 h(-1)Gbit(-1) for 40-nm SRAMs were measured for a residual machine-induced neutron flux of similar to 3.15 x 10(5) cm(-2)s(-1) below the reinforced concrete slab (thickness of 1045 mm) supporting the tokamak chamber. To complete this characterization work, a general methodology for the SER prediction in such a mixed-field D-T neutron radiation environment composed of both thermal and fast neutrons (FN) (up to 14 MeV) is presented and validated from this ensemble of experimental data for the two SRAM technologies. Finally, the interest in this approach for future tokamaks and high-energy physics accelerators is discussed.

Semiconductors characterized by ultrawide bandgaps (UWBGs), exceeding the SiC bandgap of 3.2 eV and the GaN bandgap of 3.4 eV, are currently under focus for applications in high-power and radio-frequency (RF) electronics, as well as in deep-ultraviolet optoelectronics and extreme environmental conditions. These semiconductors offer numerous advantages, such as a high breakdown field, exceptional thermal stability, and minimized power losses. This study used numerical simulation to investigate, at the material level, the single-particle radiation response of various UWBG semiconductors, such as aluminum gallium nitride alloys (AlxGa1−xN), diamond, and β-phase gallium oxide (β-Ga2O3), when exposed to ground-level neutrons. Through comprehensive Geant4 simulations covering the entire spectrum of atmospheric neutrons at sea level, this study provides an accurate comparison of the neutron radiation responses of these UWBG semiconductors focusing on the interaction processes, the number and nature of secondary ionizing products, their energy distributions, and the production of electron–hole pairs at the origin of single-event effects (SEEs) in microelectronics devices.

We present an analytical model for the lethargic neutron spectrum (ϕu(E), i.e., per unit of u=ln(E)), which is specifically suited to nuclear fusion environments. The spectrum is represented as the sum of three components: (i) a stretched Maxwellian thermal component, (ii) a windowed power-law epithermal plateau and (iii) a log-normal high-energy peak. While being simple and concise, this model allows for accurate fitting to experimental data or transport calculation results, as well as easy extrapolation for different operating conditions. We present the physical basis of the model and provide guidelines for adjusting it. We also demonstrate how it can accurately reproduce neutron spectra from experiments or Monte Carlo simulations that are representative of various nuclear fusion environments. Finally, we use this model to estimate the soft-error rate (SER) for circuits operating in fusion environments, considering, in addition, analytical forms for the single-event neutron cross-section of the circuit in the thermal and high-energy domains to derive analytical or semi-analytical expressions of the SER.

Aluminum nitride (AlN), diamond, and β-phase gallium oxide (β-Ga2O3) belong to the family of ultra-wide bandgap (UWBG) semiconductors and exhibit remarkable properties for future power and optoelectronic applications. Compared to conventional wide bandgap (WBG) materials such as silicon carbide (SiC) and gallium nitride (GaN), they demonstrate clear advantages in terms of high-voltage, high-temperature, and high-frequency operation, as well as extremely high breakdown fields. In this work, numerical simulations are performed to evaluate and compare the radiative responses of AlN, diamond, and β-Ga2O3 when exposed to neutron irradiation covering the full atmospheric spectrum at sea level, from 1 meV to 10 GeV. The Geant4 simulation framework is used to model neutron interactions with the three materials, focusing on single-particle events that may be triggered. A detailed comparison is conducted, particularly concerning the generation of secondary charged particles and their distributions in energy, linear energy transfer (LET), and range given by SRIM. The contribution of the 14N(n,p)14C reaction in AlN is also specifically investigated. In addition, the study examines the consequences of these interactions in terms of electron-hole pair generation and charge deposition, and discusses the implications for the radiation sensitivity of these materials when exposed to atmospheric neutrons.

This article aims to provide a survey of modeling and simulation of single-event effects (SEEs) in digital electronics at device, circuit, and system levels. It primarily focuses on the specific multiscale, multiphysics, multidomain nature of SEEs and on the main underlying physical mechanisms that lead to the occurrence of single events in digital devices and circuits. This article addresses different ways to model and simulate both in space and time this complex sequence of mechanisms from the particle-material interaction up to the electrical response of a given electronics device, circuit, or system. It highlights the specific features of each methodology and discusses simulation requirements, code, or model inputs and expected outputs.

In this work, the radiation response of bulk GaN and Ga2O3 materials exposed to ground-level neutrons is studied by Geant4 numerical simulation, considering the whole atmospheric neutron spectrum at sea level, from thermal to high energies (GeV). The response of the two materials is compared in terms of the number and type of interactions and the nature of the secondary products produced, particularly in nuclear reactions. Our results highlight the importance of 14N(n,p)14C neutron capture in the radiation response of GaN, leading to large differences in the behavior of the two materials in terms of susceptibility to thermal and intermediate-energy (below 1 MeV) neutrons.

In this paper, the interactions of low-energy muons (E < 10 MeV) with natural silicon, the basic material of microelectronics, are studied by Geant4 and SRIM simulation. The study is circumscribed to muons susceptible to slowdown/stop in the target and able to transfer sufficient energy to the semiconductor to create single events in silicon devices or related circuits. The capture of negative muons by silicon atoms is of particular interest, as the resulting nucleus evaporation and its effects can be catastrophic in terms of the emission of secondary ionizing particles ranging from protons to aluminum ions. We investigate in detail these different nuclear capture reactions in silicon and quantitatively evaluate their relative importance in terms of number of products, energy, linear energy transfer, and range distributions, as well as in terms of charge creation in silicon. Finally, consequences in the domain of soft errors in microelectronics are discussed.

We have performed real-time soft error rate (SER) measurements on bulk 65 nm static random-access memories (SRAMs) during deuterium–deuterium (D-D) plasma operation at W–tungsten– Environment in Steady-state Tokamak (WEST). The present measurement campaign was characterized by the production of several tens of long pulse discharges (~60 s) and by a total neutron fluence (at the level of the circuits under test) up to ~10 9 n.cm -2 , improving the error statistics by a factor of more than 6 with respect to the first measurements obtained in 2020. Experimental results demonstrate the occurrence of bursts of single-event upsets (SEUs) during the most efficient shots and 12% of multiple cell upset (MCU) events. Time-resolved data also show that MCUs are preferentially detected in the last part of these long pulses, providing further evidence that higher energy neutrons, initiated by deuterium–tritium (D-T) reactions due to triton burn-up in the D-D plasma, may play a role in the production of multiple cell upsets that cannot be attributed in such large proportions to “low energy” neutrons produced in D-D reactions.

ITER is of key importance in the European fusion roadmap as it aims to prove the scientific and technological feasibility of fusion as a future energy source. The EUROfusion consortium of labs within Europe is contributing to the preparation of ITER scientific exploitation and operation and aspires to exploit ITER outcomes in view of DEMO. The paper provides an overview of the major progress obtained recently, carried out in the frame of the new (initiated in 2021) EUROfusion work-package called 'Preparation of ITER Operation' (PrIO). The overview paper is directly supported by the eleven EUROfusion PrIO contributions given at the 29th Fusion Energy Conference (16-21 October 2023) London, UK [www.iaea.org/events/fec2023]. The paper covers the following topics: (i) development and validation of tools in support to ITER operation (plasma breakdown/burn-through with evolving plasma volume, new infra-red synthetic diagnostic for off-line analysis and wall monitoring using Artificial Intelligence techniques, synthetic diagnostics development, development and exploitation of multi-machine databases); (ii) R&D for the radio-frequency ITER neutral beam sources leading to long duration of negative deuterium/hydrogen ions current extraction at ELISE and participation in the neutral beam test facility with progress on the ITER source SPIDER, and, the commissioning of the 1 MV high voltage accelerator (MITICA) with lessons learned for ITER; (iii) validation of neutronic tools for ITER nuclear operation following the second JET deuterium-tritium experimental campaigns carried out in 2021 and in 2023 (neutron streaming and shutdown dose rate calculation, water activation and activated corrosion products with advanced fluid dynamic simulation; irradiation of several materials under 14.1 MeV neutron flux etc).

When an ionizing particle passes through a semiconductor device, it transfers energy and generates electron-hole pairs along its path. The excess carriers are subsequently transported throughout the semiconductor’s volume via ambipolar diffusion until they either recombine or are collected and extracted typically by a biased contact or a reverse-biased p-n junction. To predict the transient electrical behavior of complementary metal-oxide semiconductor (CMOS) devices and circuits when exposed to ionizing radiation and assess their soft error rate (SER), it is fundamental to accurately model these diverse physical processes. In this chapter, we present a comprehensive modeling and analysis of the diffusion and collection mechanisms of radiation-induced charges through a semiconductor device. Analytical formulations of the collected charge, collection current, and collection velocity are developed. These equations are further employed to establish an analytical formulation of the soft error rate (SER), explaining its exponential dependence on the critical charge of the circuit. This formulation also links the SER to various physical and technological parameters, as well as to the characteristics of the radiation.

The exponential dependence of the soft error rate (SER) with critical charge in CMOS circuits, empirically proposed by Hazucha and Svensson, is derived in the framework of the diffusion-collection approach. A full analytical formulation is established, linking the SER with physical and technological parameters, notably the circuit supply voltage, carrier diffusion coefficient, and ion characteristics.

Synergy effect of total ionizing dose (TID) on alpha-soft error rate (alpha-SER) in FDSOI 28 nm SRAM has been experimentally characterized using a dedicated setup combining alpha-particle irradiation (241Am solid source) in vacuum chamber and 10 keV X-ray irradiation. Measurements have been performed on a 3 Mbit single-port SRAM cut powered at 1 V. Irradiations up to 125 krad(Si) have been achieved and their impact on the alpha-SER has been characterized from the cumulated number of bitflips as a function of the exposition time to the alphasource. Modelling and simulation have been used to link transistor threshold voltage variations to SRAM cell stability in terms of static noise margin (SNM), critical charge (Qcrit) and finally estimated SER, in good agreement with experimental results.

Charge diffusion from an ion track and its collection by a biased contact in a semiconductor domain is modeled and analyzed within the framework of the so-called diffusion–collection approach. We successively examine the case of charge diffusion from a point source and from a linear distribution, introducing and discussing the concept of collection velocity at the point where the collection current is evaluated. Analytical formulations of the collected charge, collection current, and collection velocity are developed. Implications for the calculation of the soft error rate in complementary metal-oxide-semiconductor circuits exposed to ionizing particles are derived. Finally, our model provides new insights into the correct definition of the charge collection velocity in collection–diffusion models.

This numerical simulation work investigates the basic physical mechanisms of single events induced in a target layer composed of silicon carbide exposed to natural radiation with atmospheric neutrons at the terrestrial level. Using direct calculations and extensive Geant4 simulations, this study provides an accurate investigation in terms of nuclear processes, recoil products, secondary ion production and fragment energy distributions. In addition, the thorough analysis includes a comparison between the responses to neutron irradiation of silicon carbide, carbon (diamond) and silicon targets. Finally, the consequences of these interactions in terms of the generation of electron–hole pairs, which is a fundamental mechanism underlying single-event transient effects at the device or circuit level, are discussed in detail.

This work focuses on the radiation response of Group IV (Si, Ge, SiC, diamond) and III-V (GaAs, GaN, GaP, GaSb, InAs, InP, InSb, AlAs) semiconductors subjected to D–D (2.45 MeV) and D–T (14 MeV) neutrons. The response of each material has been systematically investigated through a direct calculation using nuclear cross-section libraries, MCNP6, and Geant4 numerical simulations. For the semiconductor materials considered, we have investigated in detail the reaction rates per type of reaction (elastic, inelastic, and nonelastic) and proposed an exhaustive classification and counting of all the neutron-induced events and secondary products as a function of their nature and energy. Several metrics for quantifying the susceptibility of the related semiconductor-based electronics to neutron fusions have been finally considered and discussed.

We conducted a real-time soft-error rate characterization of CMOS bulk 65-nm static random access memories (SRAMs) subjected to fusion neutrons during deuterium–deuterium (D-D) plasma operation at W–tungsten–Environment in Steady-state Tokamak (WEST). The test equipment, installed in the experimental hall at several locations of the tokamak, was irradiated during machine shots by a flux of particles dominated by primary 2.45-MeV neutrons. Real-time neutron metrology, neutron spectrometry, complementary characterization with monoenergetic neutrons, and Monte Carlo numerical simulations at both material and circuit levels have also been performed to analyze the experimental data. Our results suggest that higher energy neutrons, simultaneously produced by deuterium–tritium (D-T) reactions due to triton burn-up in the D-D plasma, play a significant role in the radiation response of SRAMs for which multiple cell upsets are detected and cannot be attributed to D-D neutrons.

We validated a method for predicting the Soft Error Rate (SER) in the WEST tokamak operated with deuterium plasmas, and we applied it to predict the SER in the ITER tokamak operated with deuterium-tritium plasmas.

The interactions of high energy neutrons produced in D-D and D-T nuclear fusion reactions with natural silicon have been investigated through direct calculation using nuclear cross section libraries, MCNP6 and Geant4 numerical simulations. From the systematic simulation and particle tracking of 5 x 10(8) neutrons incident on a 1 cm(2) x 20 mu m bulk target, we provide a detailed analysis of all interactions (elastic, inelastic, nonelastic) per type of reacting silicon isotope and an exhaustive classification of all neutron-induced secondary products as a function of their type, energy, linear energy transfer and range in silicon. Implications for reliability of the electronics in future power fusion machines are discussed based on these first evaluations.