Unveiling the Hidden Cascade: Secondary Particle Generation in Hybrid Halide Perovskites Under Space-Relevant Ionizing Radiation

Abstract

Hybrid halide perovskites are promising materials for optoelectronics and space applications due to their excellent light absorption, high efficiency, and light weight. However, their stability under radiation exposure remains a key challenge, especially in space environments, where high-energy particles can cause significant damage. Here, we present the effects of primary and secondary radiation on perovskite materials, using Monte-Carlo simulations with the GEANT4 toolkit. The interactions of protons, electrons, neutrons, and γ-rays with APbI3 (A = Ma, FA, Cs) perovskites under space-relevant conditions typical for low Earth orbit (LEO) were studied. The results show that different perovskite compositions respond uniquely to radiation: CsPbI₃ generates higher-energy secondary positrons, neutrons, and protons, while MAPbI₃ produces more secondary electrons under proton irradiation. Mixed-cation perovskites exhibit narrower energy distributions for secondary γ-rays, indicating material-dependent differences in radiation tolerance. These findings suggest the potential role of secondary particle generation in perovskite degradation, based on our simulations, and they emphasize the need for comprehensive modeling to improve the radiation resistance of perovskite-based technologies for space applications. Future studies should consider contributions from encapsulating materials in device structures.

1. Introduction

The class of perovskites is defined by the general chemical formula ABX₃, where A represents a monovalent cation, B is a divalent metal cation, and X is a non-metal anion. Hybrid halide perovskites occupy a distinctive position within this class of materials. In these compounds, A typically consists of monovalent cations such as CH₃NH₃⁺ (MA⁺), CH(NH₂)₂⁺ (FA⁺), or Cs⁺; B represents divalent metal cations such as Pb²⁺ or Sn²⁺; and X corresponds to halide anions such as I⁻, Br⁻, or Cl⁻.

In recent years, perovskite materials have demonstrated exceptional promise in the field of optoelectronics due to their outstanding intrinsic properties such as excellent light absorption, a highly tunable bandgap, high photoluminescence quantum yields, relatively simple solution synthesis, and structural flexibility [1]. These characteristics make perovskites interesting for applications in solar cells [2], light-emitting diodes (LEDs) [3,4], photodetectors [5,6], and other optoelectronic devices [6]. In particular, perovskite solar cells (PSCs) have achieved remarkable advancements, with solar energy conversion efficiencies now exceeding 26% [7,8].

Ongoing studies on halide perovskites have provided detailed insight into how composition affects stability under various external stressors. MAPbI₃ remains one of the most investigated systems due to its outstanding optoelectronic properties; however, it shows pronounced sensitivity to moisture, thermal cycling, and ionizing radiation, which accelerate defect formation and organic-cation degradation [9,10,11,12]. FAPbI₃, though offering a narrower bandgap and higher theoretical efficiency, tends to undergo phase transitions under irradiation or prolonged heating, limiting its operational stability [10,13,14]. In contrast, the inorganic CsPbI₃ phase demonstrates superior thermal and radiation robustness but suffers from structural instability at ambient conditions [12,15,16]. To overcome these drawbacks, mixed-cation compositions such as Cs_xFA_1-xPbI₃ [13,17] and Cs_xMA_yFA_1-x-yPbI₃ [12,18,19] have been developed, showing improved lattice rigidity and defect tolerance. Experimental and simulation results indicate that these mixed perovskites retain a significant fraction of their optical and electronic performance even after exposure to high-energy protons, electrons, or γ-rays, suggesting that compositional engineering can effectively balance efficiency and durability for various applications.

Recently, perovskite materials have attracted significant attention not only for terrestrial applications but also as highly promising candidates for space applications [12,20,21]. In space, the need for lightweight, efficient, and cost-effective energy-harvesting technologies is crucial [22]. Due to their high power-to-weight ratio, PSCs have emerged as strong candidates for powering satellites, spacecrafts and space stations [23]. Nevertheless, their utilization in such extreme environments poses a number of challenges: thermal cycling, exposure to ionizing radiation, and solar spectrum AM0. In space environments, perovskites are exposed to high-energy particles such as protons, electrons, neutrons and heavy ions [20,21,24]. When such materials are irradiated, they are damaged, and some defects in the structure can be produced such as vacancies, displaced atoms, electronic excitations and so on [25]. The primary particles generate secondary ones that can cause additional defects in the crystal lattice. These defects lead the device efficiency to decrease, as well as resulting in current leaks and other flaws. On the other hand, the generation of secondary particles can be a convenient channel for energy loss by cosmic radiation, preventing the creation of point defects due to the transfer of a small fraction of energy from the primary particles. In addition, secondary particles can contribute to the generation of excitons and also participate in conductivity themselves, which can lead to some improvement in properties. Thus, it is necessary to study the influence of the various particle flows in a wide energy range to the electromagnetic and hadronic processes, generation of secondary radiation, and perovskite structural defects caused by it.

Most studies of radiation effects on perovskite materials focus on the primary particle interactions with the material [26,27]. Defect formation processes such as the knock-out of atoms from the crystal lattice (Non-Ionizing Energy Loss, NIEL) and ionization processes (Ionizing Energy Loss, IEL) are mostly considered. However, it is often overlooked that a notable portion of the primary particle energy (e.g., about 41% for 0.1 MeV protons [28]) can be transferred to the secondary ones that are formed as a result of these interactions, although this fraction may vary in thin-film devices. Secondary particles such as knock-out atoms, nuclear fragments or even photons can have sufficient energy to create local damage cascades, including additional lattice defects and changes in the electronic structure and the accumulation of local heating [29]. For example, heavy nuclei formed as a result of interaction of primary neutrons or protons with the material can cause local “hot spots” where intense ionization and non-ionization processes occur. While primary radiation effects have been studied extensively, the role of secondary particles generated within the perovskite layer remains underexplored. Our simulations aim to quantify their generation, but they do not account for contributions from device encapsulants, which may dominate in real applications.

Moreover, it is especially important to take into account the protons’ and neutrons’ ability to initiate material activation, leading to radioactive isotopes generation [29,30]. These isotopes are capable of emitting γ-rays or beta particles, interacting with the material additionally, causing extra damage and local heating as well [31]. Such effects can significantly change the material characteristics and deteriorate their stability and durability, especially under conditions of long-term exposure in space environments.

Thus, to fully understand the radiation effects on perovskites, it is necessary to consider not only the primary interaction processes, but also secondary phenomena associated with energy transfer, local heating and material activation. In the present study, we investigated the processes occurring when perovskite materials are exposed by means of Monte-Carlo simulations. We paid particular attention to characteristics of secondary particles and effects that could be induced by them. This study focuses on secondary particles within bulk perovskite, but future research should extend to layered device structures, where encapsulating materials (e.g., glass or polymers) could generate dominant secondary fluxes.

2. Calculation Details

High-energy particle exposure, as well as generated secondary particles, leads to damage to the crystal structure and degradation of material properties. To determine the nature of the electromagnetic and hadronic processes, its impact on the defects, and the radiation stability of devices in the space environment, it is necessary to use both experimental research and modeling.

In this study, several types of perovskite materials representing both model single cation (MAPbI₃, FAPbI₃, and CsPbI₃) perovskites and mixed multi cation ones (Cs_0.12FA_0.88PbI₃ and Cs_0.1MA_0.15FA_0.75PbI₃) were considered. These compounds have been thoroughly studied and are widely used in research due to their high efficiency in energy conversion and relative ease of synthesis. However, their stability under the influence of external factors (including radiation) varies, which makes them suitable for the basic analysis of degradation processes. In addition, we examined mixed perovskites—the complex hybrid structures in which different cations (Cs⁺, MA⁺, FA⁺) are combined to improve the material properties. Cs_0.12FA_0.88PbI₃ exhibits high thermal stability due to the inclusion of cesium, which makes it promising for operation in high-temperature conditions [32]. On the other hand, Cs_0.1MA_0.15FA_0.75PbI₃ is characterized by a balanced combination of ease of synthesis, stability and high efficiency, which is due to the synergistic effect of mixed cations [33]. The choice of these materials is due to their diversity in their cation composition and allows one to compare the effect of radiation on the stability and properties of both single cation and complex multi-cation perovskite systems.

To thoroughly model the radiation exposure influence on these materials, a comprehensive modeling approach was adopted. By leveraging the GEANT4 toolkit (version 11.3.2) [34,35,36], the effects of various types of the ionizing radiation (protons, electrons, neutrons, and γ-rays) on perovskites with different compositions and structures were simulated. The selection of particle types and their corresponding energy ranges was carefully determined to replicate the diverse radiation environment encountered in space and the real conditions of radiation exposure in space, with four principal primary particle sources: galactic cosmic rays (GCR) from beyond the solar system, trapped in geomagnetic field energetic electrons and protons, high particle fluxes from the solar events (SEP) and albedo protons and neutrons [37,38,39,40].

The radiation environment in the low Earth orbit (LEO, approximately 160 ÷ 2000 km above the Earth’s surface) is composed of charged and neutral particles, including those from the GCRs, SEPs, and albedo neutrons. To model the effects with materials under these conditions, electrons (energies from tens of keV to several MeV), protons (energies from 1 to 100 MeV), low- and medium-energy neutrons (energies from tens, hundreds of keV to several MeV) [41,42], as well as ions (energies up to several, tens of MeV) [43], are often used.

In the medium Earth orbit (MEO, 2000 ÷ 35,786 km above the Earth’s surface), the radiation exposure essentially consists of particles from the GCRs, SEPs and radiation belts: electrons (energies up to 10 MeV), protons (energies from hundreds of MeV to several GeV), ions (energies from several MeV to several GeV), secondary γ-rays and neutrons produced in reactions and processes with different energies, depending on the primary particle energy and the type of reaction or process [42,43].

In the geostationary Earth orbit (GEO, 35,786 km above the Earth’s surface), the main sources of radiation are GCRs, SEPs (especially during flares), and the influence of radiation belts remains: electrons (energies up to 1 MeV; nevertheless, during flares and magnetospheric disturbances, energies can reach tens or hundreds of MeV), protons (energies from hundreds of keV to hundreds of GeV), ions (energies up to tens of GeV), γ-rays and neutrons are present as secondary components of radiation exposure [43].

However, high-energy particles have significantly smaller fluxes compared to lower-energy ones in the MEO and GEO [43].

To study the effects of radiation on materials, including perovskites, various methods and types of radiation are used:

• electrons—to assess the impact of high-energy particles on materials in radiation belts, to research the influence of ionizing radiation on the perovskite properties (e.g., radiation hardness) [22,44],
• protons and ions—to assess the material mechanical and radiation damage and to obtain information about the cascades of atom knockout, as well as defect formation [22,29,45,46],
• γ-rays—to assess the changes in the optical and electrical properties of materials, such as a decrease in photoluminescence or an increase in leakage currents [22,47],
• neutrons—to assess the process of atom knockout and material activation [22,48].

Thus, for the LEO conditions, we model the interaction of various types of radiation, including protons (0.05 MeV, 0.5 MeV, 3 MeV, 18 MeV, 24 MeV), electrons (0.18 MeV, 0.5 MeV, 2 MeV, 10 MeV, 60 MeV), neutrons (0.5 MeV, 1 MeV, 5 MeV, 14 MeV) and γ-rays (0.662 MeV, 1.17 MeV, 1.33 MeV) with different perovskite materials, using GEANT4 as a universal tool for simulating the passage of particles through matter. This tool allows us to analyze the mechanisms of material damage, as well as the formation of secondary particles.

The simulation was performed for thick (1 cm) perovskite materials. The typical thickness of the active perovskite layer in solar cells is 200–500 nm. However, to understand the processes occurring in such materials, it is necessary to simulate either large fluxes of incident radiation or increase the thickness of the samples. The GEANT4 software environment allows us to simulate the fluxes up to 9.9 × 10⁹ particles/cm². However, such flux value calculations require significant time and computer resources. At the same time, modeling 1 cm compared to 0.5 μm allows us to increase the number of possible events by 2 × 10⁶. Thus, the thickness of 1 cm and a flux of 10⁴ particles/cm² allows us to obtain the same number of events both in an active perovskite layer 500 nm thick and at a flux of 10¹⁰ particles/cm². This approach was chosen to establish a foundational understanding for the intrinsic potential of various perovskite compositions to generate secondary particles, isolated from the effects of other device layers. While this thick-layer approximation efficiently provides this crucial baseline, it may overestimate the volumetric density of secondary particle effects within the thin active layer of real devices. Furthermore, encapsulating materials (e.g., glass, polymers), not modeled here, could contribute significantly to secondary fluxes penetrating the perovskite, which represents the essential next step for modeling full device stacks.

In the case of heavy secondary particles such as knocked out ions and decay products, TRIM simulation was used. As initial parameters (number of ions, their energy and so on), the data obtained in GEANT4 simulation were used.

A detailed description of the simulation setup is provided in the Supplementary Materials (SI). This includes the detector geometry, material properties (density and atomic composition), and the configuration of physics models. Specifically, we employed specialized physics lists for modeling hadronic and electromagnetic interactions, defined energy thresholds for different physics models, and set appropriate production cuts to control the generation of secondary particles.

3. Results

Various particles have the ability to deposit energy in the materials and induce numerous types of effects. The interactions are substantially dependent on the particle characteristics (its charge, mass, and energy). For example, charged particles such as protons are involved in both nuclear and Coulombic interactions with the atomic nuclei and orbital electrons of the target material, consequently. In contrast, neutrons have no charge and can pass through the electronic clouds of atoms of the matter without interaction, thus interacting solely with atomic nuclei [24]. Figure S1 shows the Coulombic, nuclear and photon–matter interactions, which are essential to understanding the impact of the ionizing radiation on the primary and secondary radiation effects caused by it. The possible radiation induced processes are described in more detail in Supporting Information (SI).

First, secondary electrons could be generated by interaction of incident particles with target atoms. Such secondary electrons, depending on their energy, can participate in both further defect formation and other processes. For example, they can be captured by defects, radiative recombination could take place or of secondary electrons with low energies would contribute to conductivity.

Excited atoms can also act as centers of radiative recombination, reducing the efficiency of energy conversion.

Secondary gamma quanta and other photons will not introduce significant effects, but they can in turn cause ionization or lead to radiation-stimulated segregation, as shown in the works [47,49,50,51].

Finally, one of the most important processes is the formation of secondary heavy particles. It can occur both as a result of nuclear transformations during irradiation with neutrons and protons, and via the impact mechanism when exposed to electrons, neutrons, protons [52]. In the case of radiation transformations, decay products may also be formed that have significant initial energy, causing cascades of atomic displacements or indirect ionization [24].

Our simulated secondary particle yields and energies align qualitatively with experimental observations of radiation-induced degradation in halide perovskites. For proton fluences above 10¹³ cm⁻², studies report film darkening and reduced carrier lifetime, potentially linked to secondary electron cascades causing ionization, and defect clustering [29,53]. However, discrepancies arise in thin films, where surface effects and encapsulants alter secondary interactions, suggesting our bulk models provide a baseline for further experimental benchmarking.

Now, we will consider in more detail the influence of each type of radiation on the generation and characteristics of secondary particles.

3.1. Secondary Photons

Figure 1, Figure 2, Figure 3 and Figure 4 present the dependences of the number of secondary γ-rays per 10,000 primary particles on the energy of the primary radiation, as well as the energy distribution of secondary particles relative to the energy of primary particles for different types of radiation.

A sharper decrease in the number of secondary γ-rays is observed in the range of 0.662–1.17 MeV for primary γ-rays (Figure 1a). In general, single cation perovskites exhibit higher numbers of secondary particles compared to mixed cation systems, which demonstrate narrower ranges between minimum and maximum energies. Note the lower average energies of the generated photons in mixed perovskites. It is likely that this behavior is due to the dominating of another energy loss channel by primary particles. In particular, this may be due to the high costs of ionization, as shown below. In general, we note that, in such interactions, it is mainly X-ray photons that are generated and their number is not large. We expect that secondary photons will not significantly affect the degradation processes in the case of primary gamma-ray irradiation.

For primary electron irradiation, a more pronounced increase in the number of secondary γ-rays is evident in the energy range up to 10 MeV, while less intense growth is observed between 10 MeV and 60 MeV (Figure 2a). Notably, CsPbI₃ generates a higher number of secondary γ-rays relative to other perovskites (Figure 2f). In the energy range below 10 MeV, single-cation systems exhibit higher average energies of secondary radiation compared to three-cation systems. However, at higher energies, the averages converge to similar values across all systems. This may be because, at high energies of primary electrons (10 MeV and more), all energy loss channels are saturated. In particular, at an energy of 60 MeV, electrons can pass through even a 1 cm thick sample (Figure S2). On the other hand, at low energies of exciting particles, losses in certain channels will dominate over the others. In the case of multi-cation perovskites, the appearance of secondary photons is not the main mechanism, either for primary gamma rays or for electrons.

However, for cases of exposure to neutrons and protons, the picture is significantly different, which is obviously due to the difference in the processes of particle interactions with matter (Figure S1). For proton irradiation, the number of secondary γ-rays increases most significantly for MAPbI₃ and mixed-cation perovskites (Figure 3).

At lower proton energies, secondary γ-rays are not observed. The average energy of secondary particles is higher for mixed-cation systems, while CsPbI₃ demonstrates the lowest average energy. FAPbI₃ exhibits the widest range between minimum and maximum values. At 24 MeV, MAPbI₃ and mixed-cation perovskites show higher average energies compared to other single-cation systems, which exhibit comparable averages and ranges between minimum and maximum values.

Under neutron irradiation (Figure 4), an increase in the number of secondary γ-rays is observed in the primary energy range of 0.5–5 MeV, with a more pronounced growth seen above 5 MeV across all systems. However, for CsPbI₃, the growth is less steep.

The energy distribution of secondary particles shows similar average values as for primary protons and ranges between minimum and maximum values across all systems. At higher energy levels (at 14 MeV), the range between minimum and maximum values is narrower for CsPbI₃ compared to other perovskites.

Secondary photons are most effectively excited by electrons. At the same time, primary gamma rays and neutrons generate photons less effectively and are essentially not produced when exposed to protons. However, when exposed to neutrons and protons, only gamma quanta occur, while, when exposed to gamma rays and electrons, X-rays are produced. This is due to the processes of interaction of different types of production by matter. The exception is fast electrons (60 MeV), the energy of which is sufficient to initiate nuclear transformations with the formation of secondary gamma quanta. Finally, we note the differences in the generation of secondary photons in perovskites depending on their composition. Thus, the smallest number of photons moves in mixed perovskites, which may indicate their greater radiation resistance.

3.2. Secondary Neutrons

Figure 5 and Figure 6 present the dependences of the number of secondary neutrons per 10,000 primary particles on the energy of the primary radiation, as well as the energy distribution of secondary particles relative to the energy of primary particles for different types of radiation.

Under neutron irradiation (Figure 5), a sharp increase in the number of secondary particles is observed in the energy range of 0.5–1.0 MeV (almost two folds), followed by a decrease in the growth rate in the energy range of 1–5 MeV, and a further reduction from 5 to 14 MeV. Among all perovskites, CsPbI₃ generates the highest number of secondary neutrons, while Cs_0.1MA_0.15FA_0.75PbI₃ exhibits the lowest number in the energy range of 0.5–5.0 MeV. The energy distribution of secondary particles is approximately the same across all perovskites. The generated secondary fast neutrons can also lead to the formation of point defects and nuclear transformations, disrupting the local atomic structure of perovskites and creating carrier traps.

It is worth noting that all samples containing light elements (as part of the organic cation) are more stable in terms of secondary particle generation. On the one hand, this can be explained by the fact that light elements have high cross-sections of interaction with neutrons, which leads to frequent elastic scattering and the formation of knocked-out atoms (as shown in Section 3.4). On the other hand, heavy elements such as Cs and I can undergo nuclear transformations under the influence of fast neutrons. Several of the resulting isotopes have a probability of decay with the formation of a secondary neutron. However, both the probability of such decay and the probability of the formation of unstable isotopes with the formation of a secondary neutron in the process of decay are not high (other particles are predominantly formed, as shown below).

Under proton irradiation (Figure 6), an increase in the number of generated secondary neutrons is observed in the energy range of primary protons from 18 to 24 MeV, with the most significant growth seen for MAPbI₃ and mixed perovskite materials. On the other hand, the number of secondary neutrons generated is extremely small.

At 18 MeV, CsPbI₃ exhibits the highest average energy of secondary neutrons. For MAPbI₃ and mixed systems, the range between minimum and maximum energies is narrower compared to other perovskites. At 24 MeV, CsPbI₃ again shows the highest average energy of secondary neutrons, while the mixed perovskites exhibit a smaller range between minimum and maximum energy values of secondary particles.

Thus, despite the high energies of the secondary neutrons formed, their number is small. Accordingly, their contribution to the degradation of the perovskite material will not be large, and it is not worth considering them as one of the important channels. Note also that, when primary neutrons are irradiated a perovskite samples, the secondary particles are predominantly gamma rays and neutrons (Figure S3). Based on Figure 4 and Figure 5, we can conclude that the loss channel with the formation of secondary particles when perovskites are exposed to neutrons will not be of decisive importance.

3.3. Secondary Charged Particles

Figure 7, Figure 8, Figure 9, Figure 10, Figure 11 and Figure 12 present the number of generated charged (secondary electrons—red bars, and protons—blue ones) particles under numerous types of primary particle irradiation for the perovskite materials in the GEANT4 toolkit.

The observed decrease (Figure 7a) in the total number of secondary electrons with increasing primary γ-ray energy can be understood in terms of the changing dominance of underlying interaction processes. At lower energies, the photoelectric effect prevails: γ-quanta are fully absorbed by high-Z atoms (e.g., Cs, Pb), ejecting tightly bound electrons and triggering subsequent effects (e.g., Auger electron emission).

As energy rises into the 0.662–1.17 MeV range, Compton scattering becomes the main channel, producing recoil electrons whose yield gradually falls off with increasing γ-energy. Once the photon energy exceeds the pair-production threshold (1.022 MeV), a growing fraction of interactions produce electron–positron pairs rather than simple ionization; this both reduces the count of ejected electrons per incident photon and introduces annihilation γ-rays instead of additional electrons, accentuating the decline observed between 1.17 and 1.33 MeV.

Moreover, since the photoelectric and Compton cross-sections scale with atomic number, CsPbI₃ perovskite generates a larger number of secondary electrons compared with single organic-cation and mixed-cation compositions, where the effective Z is lower. In the single-cation perovskites (Figure 7b,c,f), the average energy of secondary particles is noticeably lower, while in the mixed systems (Figure 7d,e) it becomes roughly twice as high. This behavior can be attributed to reduced multiple scattering and weaker subsequent interactions within the more compositionally heterogeneous lattice, allowing individual electrons to retain a larger share of the photon energy and thus forming fewer but more energetic secondary particles.

Therefore, although gamma rays themselves do not induce a significant defect yield, and perovskite materials exhibit high radiation tolerance to gamma irradiation up to extreme doses [54], the secondary (Compton) electrons possess sufficient energy to create radiation defects. Furthermore, even relatively low-energy electrons (~40 keV) are capable of causing localized thermal heating of the crystal lattice and inducing localized structural damage within the solar cell [55]. Consequently, the energy dissipation channel of gamma radiation via secondary electron generation must be considered critically important. We consider tracks of gamma-rays on Figures S2 and S3, which show that gamma-rays pass through perovskites mainly without scattering. This implies that the effects of gamma irradiation can be effectively modeled experimentally using low-energy electron beams, which constitutes a significantly simpler and safer methodological approach.

Furthermore, the secondary photons and electrons generated in our simulations may induce phase segregation in mixed-cation perovskites, a phenomenon where halide ions migrate under irradiation, leading to iodine-rich and bromine-poor domains that alter bandgap and carrier recombination. This is particularly relevant for proton and electron irradiation, where high secondary electron yields (as seen in Figure 8, Figure 9 and Figure 10) could accelerate local heating and ion diffusion. Experimental studies on X-ray and electron-exposed perovskites have demonstrated such segregation, resulting in reduced photoluminescence and device efficiency. In our models, mixed perovskites show broader energy distributions for secondary particles, which may exacerbate this effect compared to single-cation systems [56,57]. While our bulk simulations suggest this potential, thin-film devices with encapsulants might experience amplified segregation due to interface effects, warranting further investigation.

For electron irradiation (Figure 8), the yield of secondary electrons rises steeply with primary energy up to about 10 MeV (Figure 8a), driven by the combined effect of increasing ionization losses, growing bremsstrahlung production (whose secondary photons (X-rays) generate electrons via the photoelectric and Compton processes), and subsequent effects. In CsPbI₃ this rapid rise is especially pronounced, giving it a substantially higher electron yield in this regime than other perovskites (due to the higher effective Z-number). Beyond 10 MeV, however, the rate of increase slows and eventually plateaus—as the ionization losses falls off at relativistic energies, further ionization becomes less efficient and high-energy bremsstrahlung photons begin to exceed photonuclear reaction thresholds (tens of MeV), opening channels that consume photon energy without directly producing the electrons (see SI, Tables S1–S4). Nevertheless, the shape of the secondary-particle energy spectrum remains effectively identical across all perovskite compositions throughout the full energy range (Figure 8b–f).

Under neutron irradiation, the number of secondary electrons increases steadily in the 0.5–5 MeV range and exhibits a pronounced rise above 5 MeV (Figure 9a). This behavior can be attributed to the nature of neutron–matter interactions. Unlike charged particles, neutrons interact predominantly with nuclei through elastic and inelastic scattering, as well as nuclear capture at low energy. These processes can excite the target nuclei or convert them into unstable isotopes, which subsequently de-excite via γ-emission. The emitted γ-rays can then generate secondary electrons through the photoelectric effect, Compton scattering, additional effects and their cascades, depending on their energy. At higher neutron energies, inelastic channels become more significant, often leading to the emission of secondary charged particles such as protons, α-particles, deuterons, or even heavier nuclear fragments. These energetic ions contribute additional ionization along their tracks, initiate bremsstrahlung emission, and drive further secondary cascades, thereby enhancing the total number of generated electrons.

The sharp rise in secondary electron yield above 5 MeV corresponds to the onset of these inelastic nuclear reaction channels, as many reaction thresholds are exceeded in this energy range. Although the mechanisms are complex, the total number of secondary electrons remains relatively similar across different perovskites. This suggests that the high-Z components (e.g., Pb and I), which are common to all studied materials, dominate the interaction cross sections and contribute significantly to electron generation via γ-ray production and subsequent secondary processes. However, while the total yields are comparable, the energy distributions of secondary electrons exhibit noticeable differences between perovskite types (Figure 9b–f). In all cases, the mean energy of secondary electrons peaks at the 5 MeV energy of neutrons coinciding with the energy range where inelastic nuclear reactions and thus the production of energetic secondary particles are most prominent. At 14 MeV, despite a higher total number of electrons, the mean energy decreases. This counterintuitive effect can be attributed to the dominance of highly energetic reaction products (such as nuclear fragments or cascade electrons) that lead to broad energy distributions, in which the majority of electrons are of relatively low energy, while only a few reach high energies. This results in a large energy spread (up to ~6 MeV) but low average energies (~5–6 keV), as seen in the energy distribution histograms. The broadening of the energy spectrum at 14 MeV also points to the development of complex secondary cascades, in which energetic ions or recoil nuclei trigger additional ionization events and produce low-energy electrons. While these cascades boost the total yield, they effectively dilute the average energy.

For the mixed-cation perovskites, such as Cs_0.12FA_0.88PbI₃ and Cs_0.1MA_0.15FA_0.75PbI₃, the energy distribution (Figure 9d,e) appears slightly broader at higher neutron energies, particularly at 14 and 5 MeV, respectively. These small differences may arise from the presence of light elements (C, H, N), which contribute to neutron moderation via elastic scattering. Slower neutrons are more likely to undergo capture or trigger low-threshold reactions, potentially leading to subtle changes in the nature and energy of secondary particles.

In summary, the secondary electron yield under neutron irradiation is governed by a combination of nuclear interactions, material composition, and cascade effects. The total number of secondary electrons increases with incident neutron energy, while the energy distribution reflects both the nature of the nuclear reactions involved and the efficiency of secondary processes such as ionization and bremsstrahlung. It is worth noting the very small average energies, which is associated both with cascade processes and with the fact that primary neutrons have a small ionization cross-section, poorly interact with the electron shell and transmit small part of energy. Thus, in this case, secondary electrons can be ignored for further investigations.

In the case of proton irradiation (Figure 10), no secondary electrons are observed at low incident energies (0.05–3 MeV), while a marked increase in secondary electron yield occurs in the 18–24 MeV range. This threshold-like behavior is expected, as low-energy protons primarily lose energy through direct ionization/excitation and are less likely to generate energetic secondaries capable of inducing cascades. At higher energies, however, protons are energetic enough to initiate a broad spectrum of interactions, including ionization, bremsstrahlung radiation, and various nuclear reactions, which in turn generate a range of secondary particles (see Figure S4), including electrons.

Bremsstrahlung photons emitted by high-energy protons in the Coulomb fields of high-Z nuclei can induce photoelectric absorption, Compton scattering, and pair production, all of which contribute to the generation of secondary electrons which can clearly be seen in Figure S4b at the tracks ends of the secondary photons and in the places of their scattering (examples are circled in red).

Additionally, at proton energies above 10–15 MeV, nuclear interactions become increasingly significant. These include inelastic scattering, spallation, (p,n), (p,α), and other proton-induced nuclear reactions, which may leave nuclei in excited states [29]. The excited nuclei can subsequently decay by emitting γ-rays or charged particles, further fueling secondary cascades. Some of these emitted γ-rays may also exceed thresholds for photoneutron or photoparticle reactions, especially in high-Z elements such as Pb and I, thus compounding the overall production of ionizing radiation.

Among the materials studied, MAPbI₃, Cs_0.12FA_0.88PbI₃, and CsPbI₃ show the most pronounced increase in secondary electron production at higher proton energies (Figure 10a). This may be linked to the presence of heavier elements and the relative efficiency of interaction processes within their specific compositions. While the cross sections for many nuclear and electromagnetic interactions tend to increase with Z, particularly for bremsstrahlung and photon-induced processes, exact behavior can vary depending on the energy range and reaction channel. For the 18–24 MeV range, it is plausible that higher-Z components in these perovskites contribute more effectively to bremsstrahlung and subsequent secondary processes, compared to compositions with lighter atoms.

Moreover, structural and electronic properties such as crystal packing, local density, and energy transfer efficiency can modulate the cascade behavior and facilitate efficient secondary particle generation even in perovskites with organic components. In some cases, light atoms may even enhance the density of low-energy ionization events, contributing to a larger overall electron yield.

Secondary electrons generated under various types of radiation may participate in the radiolysis of the organic components in hybrid perovskites, such as methylammonium (MA) or formamidinium (FA) cations. Radiolysis involves the dissociation of chemical bonds due to ionizing radiation, potentially leading to the formation of volatile species, phase segregation, or defect accumulation in the organic-inorganic framework. For instance, low-energy secondary electrons can excite or ionize the organic molecules, promoting reactions like hydrogen abstraction or carbon-nitrogen bond cleavage, which compromise the structural integrity and optoelectronic properties of the material [25,56]. This effect has been observed in studies on X-ray-induced degradation, where secondary electrons contribute to lattice defects and instability in organic-inorganic halide perovskites [56]. While our simulations quantify the generation of such electrons, experimental validation is needed to assess their precise role in radiolysis processes.

In addition to potential degradation, secondary particles, particularly low-energy electrons and protons, may facilitate self-healing mechanisms in hybrid perovskites. These processes involve ion migration and defect passivation, where radiation-induced excitations promote the reconfiguration of the lattice, potentially mitigating point defects such as vacancies or interstitials. For instance, studies have shown that halide perovskites exhibit remarkable recovery after proton or gamma irradiation, attributed to the dynamic nature of organic-inorganic interfaces that allow for self-repair at room temperature [31]. Our simulations indicate that secondary electrons with energies below 10 keV could contribute to such excitations without causing extensive cascades, suggesting a dual role in both damage and recovery. However, this remains speculative and requires experimental validation in device contexts.

Although the overall energy distributions of secondary particles remain broadly similar across all perovskites (Figure 10b–f), MAPbI₃ exhibits a higher mean energy and a wider min–max spread, indicating a larger share of high-energy secondaries in this system. Additionally, Cs_0.12FA_0.88PbI₃ shows a notably broader energy distribution at 18 MeV and the highest maximum energies at 24 MeV, suggesting enhanced cascade effects or the presence of higher-energy nuclear fragments in this material. On the other hand, the number of generated particles is not large and such fluctuations can be caused by individual emissions.

Under neutron irradiation (Figure 11), a noticeable decline in the number of secondary protons is observed across the studied energy range (Figure 11a). This decrease is most pronounced in the low-energy range of 0.5–1 MeV, less steep between 1 and 5 MeV, and becomes more gradual and monotonic from 5 to 14 MeV.

Notably, in the case of CsPbI₃, no secondary protons are detected until the primary neutron energy reaches 14 MeV, at which point a small number of protons are produced. The observed decline in secondary proton production with increasing neutron energy, while counterintuitive given the opening of more reaction channels, can be explained by the energy dependence of neutron reaction cross-sections. In the MeV energy range, the cross-sections for exothermic proton-emitting reactions (e.g., (n,p) on light nuclei) often decrease rapidly with energy. While new channels such as (n,2p) open, their thresholds are high and their cross-sections remain relatively small. Consequently, the dominant interaction for fast neutrons in these materials is elastic and inelastic scattering, which does not directly produce secondary protons. The probability of a neutron undergoing a proton-producing nuclear reaction thus decreases as its energy increases, leading to the observed reduction in yield.

This behavior may be attributed to the lack of light elements in the perovskite, which are known to be effective moderators for slowing down fast neutrons. In mixed perovskites containing MA⁺ or FA⁺ cations, light atoms can efficiently reduce neutron energies through elastic scattering, thereby increasing the probability of subsequent interactions such as (n,p), (n,2p) and nuclear reactions with target nuclei. In CsPbI₃, however, the absence of such light atoms results in a lower probability of neutron thermalization, meaning that fast neutrons are less likely to be captured or to trigger proton-emitting reactions before passing through the material.

Moreover, the production of secondary protons can also occur indirectly via photonuclear reactions, where high-energy γ-rays (generated, for instance, through inelastic neutron scattering or neutron capture followed by gamma decay) induce reactions such as (γ,p) on nearby nuclei. These channels may be active at higher incident neutron energies, but their cross sections are typically small and highly energy-dependent, which is consistent with the relatively low yield of secondary protons observed even at 14 MeV.

Interestingly, while the total number of secondary protons in CsPbI₃ remains low, their average energy (Figure 11f) at 14 MeV is nearly twice as high as in other perovskites (Figure 11b–e). Additionally, the energy spread is almost three times narrower, suggesting that the few protons produced are likely the result of discrete high-energy reaction channels with more well-defined kinematics, rather than broad-spectrum cascades involving many low-energy interactions.

Overall, the decline in secondary proton production with increasing neutron energy may also reflect the reduced interaction probability of fast neutrons, which are more likely to traverse the material without significant nuclear interaction. This trend, along with the pronounced material dependence, highlights the importance of both elemental composition and neutron moderation effects in governing secondary particle yields under neutron irradiation.

Finally, under proton irradiation (Figure 12a), a significant increase in the number of secondary protons is observed for MAPbI₃ and FAPbI₃ in the energy range of 18–24 MeV, whereas the growth is more monotonic and moderate for mixed-cation perovskites. In contrast, for CsPbI₃, only a small number of secondary protons are detected even at 24 MeV, indicating limited nuclear activity.

This behavior reflects the underlying physics of proton–matter interactions. At low proton energies, the particles are mostly absorbed through ionization and elastic scattering, without having enough energy to surpass the reaction thresholds for nuclear processes such as (p,n), (p,γ), or other proton-induced reactions. As the energy of incident protons increases above 10–15 MeV, nuclear reactions become more probable, leading to the emission of secondary nucleons, including protons and neutrons. Additionally, high-energy protons can also generate bremsstrahlung radiation, which may initiate photonuclear reactions, such as (γ,p), further contributing to the observed secondary proton yield.

The higher yield in MAPbI₃ and FAPbI₃ can be attributed to their higher content of light elements, which not only facilitate more efficient energy deposition via ionization but also enable certain reaction channels that are less likely in heavier-element-dominated materials like CsPbI₃. Moreover, light nuclei serve as more effective targets for direct nuclear knock-out or exchange reactions.

Regarding energy characteristics (Figure 12b–f), the average energy of secondary protons remains within a similar range for all perovskites except CsPbI₃, where the average energy at 24 MeV incident protons is more than twice as high, and the energy spread is approximately three times narrower. This suggests that, in the perovskite, secondary protons are produced via specific, energetically constrained channels, likely to involve fewer but more energetic interactions. In contrast, the broader energy range seen in MAPbI₃ (at 24 MeV) and FAPbI₃ (at 18 MeV) points to a more diverse set of interaction pathways, including multi-step nuclear cascades and a wider distribution of energy transfers.

It is known that positrons could be produced under the influence of high-energy particle beams, plasma flows, and laser radiation [58,59,60]. The number of generated positrons and their energy distribution under primary electrons and γ-rays are provided in SI, Figures S5 and S6.

Under γ-ray irradiation, the number of positrons increases with the energy of the primary radiation, with more pronounced growth observed for single-cation perovskites, which generally produce a higher number of particles. This behavior is associated with the onset of pair production, a process that becomes energetically possible when the energy of the incident photon exceeds 1.022 MeV. As the primary γ-ray energy increases beyond this threshold, the probability of pair production rises, especially near high-Z atoms.

While the average energy values of the secondary positrons are approximately the same across all systems, FA-containing perovskites exhibit slightly higher average secondary particle energies at 1.17 MeV, along with narrower energy ranges. At higher energies (1.33 MeV), perovskites without Cs demonstrate slightly higher average secondary positron energies, possibly due to differences in material composition affecting photon attenuation and interaction probabilities.

Under electron irradiation, an increase in the number of positrons is observed in the energy range of 10 to 60 MeV, with the most significant growth seen for CsPbI₃. In this case, positrons are primarily produced indirectly, through bremsstrahlung radiation emitted by high-energy primary electrons as they decelerate in the Coulomb fields of nuclei. These bremsstrahlung photons can then exceed the pair production threshold and give rise to positrons via the same mechanisms as in γ-irradiation. Additionally, Compton scattering and subsequent photon cascades may contribute to the generation of sufficiently energetic photons capable of inducing pair production.

Although the average energy and the range between minimum and maximum values are approximately the same across all perovskite systems, CsPbI₃ shows the highest average positron energies at both 10 and 60 MeV. This may be attributed to its higher content of high-Z elements, which enhance both bremsstrahlung emission and the efficiency of photon–matter interactions leading to pair production.

In general, it can be concluded that, among all the secondary charged particles formed, attention should be focused primarily on electrons, as their quantity is significant and their energies are such that they effectively interact with the perovskite lattice. On the other hand, all the cases considered above involve inelastic interactions. In the case of elastic interactions with fast particles, recoil atoms and cascades of atomic displacements will be formed [52], leading to local disordering, degradation of perovskites, and alterations in their electrophysical characteristics. Such interactions are discussed in more detail in the following section.

3.4. Secondary Heavy Particles

The information about the number of generated heavy particles and their energy distribution under primary high-energetic electrons (60 MeV), protons (18, 24 MeV), and neutrons is presented in Tables S1–S7 in SI.

As ions penetrate the perovskite material, their energy gradually decreases due to interactions with the lattice atoms. This leads to a reduction in their ability to induce ionization, create vacancies, and generate phonons. At a critical depth, the ion energy becomes insufficient to sustain these processes, resulting in a decline in the corresponding quantities.

Figure 13, Figure 14 and Figure 15 present the SRIM simulation results for ¹²C, ¹⁴N, and ¹²⁷I ions in perovskite materials. For calculations, we use the average energy of atoms taken from the Geant4 study (Table S7) for more probable ions.

The ionization loss profiles for ¹²C (Figure 13) and ¹⁴N (Figure 14) extend deeper into the material compared to those for ¹²⁷I ions (Figure 15), which is in good agreement with the theory of atomic displacements (see Figure S7). This is explained by the fact that carbon and nitrogen are significantly lighter and possess higher initial energies than iodine ions.

Consequently, they penetrate further and sustain ionization over a longer path. In multi-cation perovskite systems, the ionization losses for carbon and nitrogen are slightly reduced compared to single-cation analogues, which may be attributed to the altered electronic structure and density of the mixed composition. However, for iodine ions, the opposite trend is observed—ionization losses slightly increase in mixed-cation structures, potentially due to enhanced electronic stopping associated with the more complex atomic environment. Moreover, this may be due to radiation-induced phase separation in the case of multi-cation perovskites.

The vacancy distribution also exhibits a strong dependence on the ion type. For carbon and nitrogen, the peak concentration of vacancies shifts toward greater depths, approaching the ions’ projected ranges. In contrast, for iodine, the vacancy peak is located at a shallower depth, followed by a steep decline. Notably, the total number of vacancies induced by iodine ions is nearly twice as high as that from carbon or nitrogen. This can be explained by the higher mass of iodine, which results in more efficient momentum transfer and thus more intense nuclear collisions. Interestingly, despite having slightly lower energy, carbon ions still create a significant number of vacancies. This behavior may be related to the broader Bragg peak for lighter ions, where energy deposition occurs over a longer path, sustaining continuous displacement damage. For nitrogen, both energy and mass contribute to a higher vacancy yield, which is consistent with expectations. In mixed-cation perovskites, the total number of vacancies is higher than in single-cation systems, likely due to the presence of different cations, which facilitate radiation-induced phase segregation and easier displacement.

The phonon generation profiles follow trends similar to those of vacancy production. For carbon and nitrogen ions, the phonon peaks are shifted deeper into the material, whereas, for iodine ions, they occur at shallower depths, with a rapid decrease thereafter. This correlation is reasonable, as both phonons and vacancies are generated primarily through elastic collisions with lattice atoms.

Finally, the projectile range of the ions is determined by their mass and initial energy. Carbon and nitrogen ions, being lighter and having higher kinetic energies, exhibit longer ranges in the material. In particular, the range of nitrogen ions appears most pronounced in the Cs_0.1MA_0.15FA_0.75PbI₃ perovskite, followed by FAPbI₃. For iodine ions, the projectile range increases with increasing initial energy, as expected for heavier ions that lose energy more rapidly and travel shorter distances under comparable conditions.

The irradiation of perovskite materials by secondary ions leads to the formation of various types of defects, predominantly vacancies and interstitials, which are typical for displacement damage processes.

Vacancies may occur on organic, inorganic, or mixed cations, depending on the ion energy, mass, and the local bonding environment. Lighter ions such as carbon and nitrogen, due to their higher penetration depths and extended Bragg peaks, tend to create more distributed and less localized damage, forming lower-density defect regions. In contrast, heavier iodine ions induce more concentrated damage near the surface, with significantly higher defect densities, especially in the initial few hundred nanometers of the material.

The overall intensity of structural damage correlates with both the total number of vacancies and the ion energy loss profile. Simulations indicate that iodine irradiation can lead to almost twice as many vacancies as carbon or nitrogen, suggesting a higher degree of structural disruption, including potential breaking of the Pb–I framework or collapse of the perovskite lattice in localized regions. Furthermore, the increased number of phonons generated under iodine irradiation also implies enhanced lattice vibrations, which can contribute to defect migration and lattice destabilization.

Regarding radiation tolerance, mixed-cation perovskites appear more resistant compared to single-cation ones, the presence of multiple cations (such as Cs⁺, MA⁺ or FA⁺) provides a more disordered and energetically buffered environment, which can better accommodate defect formation and reduce the likelihood of long-range structural collapse. Additionally, the inorganic Cs⁺ cation enhances lattice stiffness and improves thermal and radiation stability. In contrast, single-cation perovskites such as MAPbI₃ or FAPbI₃ with their softer lattices and higher content of volatile organic species, are more prone to damage accumulation and degradation under ion irradiation. This is particularly evident under heavy-ion bombardment, where localized heating and displacement can trigger decomposition of the organic components and phase instability.

In summary, the extent and type of defects induced by secondary ion irradiation vary with ion species and perovskite composition. Lighter ions produce more dispersed damage with moderate defect densities, whereas heavier ions like iodine cause dense damage regions with high vacancy concentrations. Mixed-cation perovskites demonstrate enhanced radiation resistance due to their structurally heterogeneous and mechanically robust lattice, making them more promising for applications in radiation-rich environments.

4. Conclusions

The simulation results reveal distinct patterns of secondary particle generation in hybrid halide perovskites under various types of ionizing radiation (γ-rays, electrons, neutrons, and protons). These secondary particles may act as significant contributors to radiation-induced damage, initiating ionization, atomic displacements, and cascade effects based on our GEANT4 and SRIM simulations.

Among all radiation types, high-energy electrons and protons (>10–15 MeV) are the most effective at generating dense secondary cascades, including both charged particles and high-energy photons, leading to a high probability of defect formation via ionization and displacement processes. Neutron irradiation, especially at energies above 5 MeV, induces additional nuclear reactions that produce energetic charged fragments, further contributing to structural damage.

In terms of radiation hardness, the all-inorganic CsPbI₃ demonstrates higher yields of secondary electrons and positrons under high-energy γ and electron irradiation, which may increase its susceptibility to ionization-driven degradation. However, its relatively narrow energy distributions for secondary protons and the lower probability of neutron moderation (due to the absence of light elements) suggest fewer displacement cascades, potentially leading to better structural stability under neutron and proton irradiation compared to organic-containing counterparts.

Mixed-cation perovskites such as Cs_0.12FA_0.88PbI₃ and Cs_0.1MA_0.15FA_0.75PbI₃ exhibit broader and more energetic secondary particle spectra, indicating stronger cascade effects and more diverse defect formation pathways, especially under neutron and proton exposure. Meanwhile, single-organic cation systems (MAPbI₃, FAPbI₃) are more prone to generating high-energy secondaries due to their content of light elements, which promote neutron moderation and increase the likelihood of damaging low-energy interactions and complex secondary cascades.

In conclusion, the radiation tolerance of perovskite materials depends on both their atomic composition and the type and energy of the incident radiation. CsPbI₃ may exhibit better resistance to displacement damage under neutron and proton irradiation, while mixed and single organic-cation perovskites are more susceptible to radiation-induced defect formation due to enhanced cascade dynamics and neutron moderation effects. These insights provide a foundation for improving radiation resistance, but experimental validation and full-device modeling are essential.

Our study is limited to secondary particles generated within the perovskite material itself and does not account for those from encapsulating layers in device structures, which may dominate in space environments. Future research should integrate these effects to better predict device failures in low Earth orbit and beyond.