Radiation-Induced Degradation Mechanisms in Silicon MEMS Under Coupled Thermal and Mechanical Fields

Abstract

Silicon-based MEMS devices are essential in extreme radiation environments but suffer progressive reliability degradation from irradiation-induced defects. Here, the generation, aggregation, and clustering of defects in single-crystal silicon were systematically investigated through molecular dynamics (MD) simulations via employing a hybrid Tersoff–ZBL potential that was validated by nanoindentation and transmission electron microscopy. The influences of the primary knock-on atom energy, temperature, and pre-strain state on defect evolution were quantified in detail. Frenkel defects were found to cause a linear reduction in the Young’s modulus and a nonlinear decline in thermal conductivity via enhanced phonon scattering. To link atomic-scale damage with device-level performance, MD-predicted modulus degradation was incorporated into finite element (FE) models of a sensing diaphragm. The FE analysis revealed that modulus reductions result in nonlinear increases in deflection and stress concentration, potentially impairing sensing accuracy. This integrated MD–FE framework establishes a robust, physics-based approach for predicting and mitigating irradiation damage in silicon-based MEMS operating in extreme environments.

1. Introduction

With the rapid advancement of nuclear energy technologies, nuclear power plants are playing an increasingly significant role in the global energy mix [1]. As critical components for monitoring key operational parameters, nuclear-grade pressure transmitters have a direct impact on the safety and stability of nuclear power systems [2]. In this context, silicon-based capacitive pressure sensors, which rely on single-crystal silicon diaphragms, have emerged as core elements of these transmitters due to their high elastic modulus, mechanical stability, and compatibility with semiconductor fabrication processes [3]. Their sensing principle is based on the slight deformation of the silicon membrane under external pressure, which is converted into measurable electrical signals for precise pressure detection [4]. While these devices perform reliably under conventional conditions, their functionality degrades severely in radiation-intensive environments—such as nuclear reactors, deep space missions, and high-energy particle accelerators—where structural integrity and sensing capability are compromised by high-dose irradiation, posing a significant challenge to their long-term reliability [5]. However, in radiation-intensive environments, irradiation-induced defects in the silicon lattice can alter elastic properties, leading to calibration drift, reduced sensitivity, and premature failure of the diaphragm. Such degradation mechanisms are not yet fully understood at the atomic scale, particularly under mechanical loads.

Numerous studies have investigated device-level performance degradation by correlating it with the underlying microstructural evolutions induced by irradiation. Gkotsis et al. [6] and Belwanshi et al. [7] investigated the effects of γ-ray exposure on silicon-based Micro-Electro-Mechanical System (MEMS) pressure sensors, and they found that radiation doses exceeding 10 Mrad led to, along with increased hysteresis and zero-point drift, a pronounced decline in sensitivity. These studies primarily quantified performance degradation at the macroscopic level. At the microscopic scale, Costantini et al. [8] and Bikerouin et al. [9] employed transmission electron microscope (TEM) and Raman spectroscopy to reveal amorphization, dislocation loops, and significant changes in surface morphology in irradiated silicon, noting strong dependencies on thermal conditions. However, these findings were mostly based on stress-free or statically loaded samples, limiting their applicability in complex stress fields. These limitations highlight the need to further explore how stress evolves under irradiation and how it couples with microstructural damage in silicon films.

Regarding stress evolution during irradiation, Norris et al. [10] developed an anisotropic plastic flow model to explain stress-driven surface patterning in silicon films subjected to low-energy ion bombardment. Similarly, Habermehl et al. [11] observed stress variations in silicon thin films under medium-energy ion irradiation across different temperature regimes, highlighting the interplay between defect formation and stress relaxation. While these works provided useful insights into stress–irradiation coupling, their focus remained largely on, without detailed investigation of defect types and their evolution within the crystal lattice, surface stress relief or ripple formation. Additionally, Klanner et al. [12] and Donegani et al. [13] systematically studied the formation mechanisms and annealing behavior of point and cluster defects in single-crystal silicon under various particle types and energy levels using techniques such as thermally stimulated current (TSC) to quantify activation energy spectra. Although these efforts laid a foundation for understanding microstructural changes under irradiation, they did not consider the role of thin-film geometry or mechanical stress. Zhu et al. [14] and Ahammou et al. [15] conducted molecular dynamics simulations to investigate thermally induced stress and microstructural evolution at the Si/SiO₂ interface during heating, while earlier works on Mo–Si annealing [16,17,18,19] and residual stress in TiNi thin films [20,21,22,23,24] explored stress transitions due to phase changes and thermal mismatch. Despite their contributions to stress–temperature–structure relationships, these studies remain insufficient for elucidating the link between irradiation-induced defects and device-level performance degradation. In summary, although considerable progress has been made in identifying point defects, modeling thin-film stress evolution, and evaluating macroscopic performance under radiation, a comprehensive understanding of defect dynamics in single-crystal silicon piezoresistive membranes subjected to combined radiation, thermal, and mechanical fields is still lacking.

In contrast, this work introduces a novel, integrated multi-scale framework that explicitly bridges this gap. Our approach combines molecular dynamics (MD) simulations, to capture atomic-scale defect generation and clustering, with finite element (FE) modeling, which propagates these microstructural changes to predict macroscopic device performance. This is further validated by nanoindentation and TEM experiments, ensuring a robust and physically grounded predictive capability. By directly embedding MD-derived mechanical property degradation (e.g., Young’s modulus reduction) into FE models, our methodology moves beyond purely empirical approaches to provide a direct, mechanistic understanding of how radiation-induced defects impair the long-term reliability of MEMS devices.

2. Materials and Methods

2.1. Molecular Dynamics Simulation

MD simulations were conducted using the LAMMPS package (lammps-22Jul2025) to investigate irradiation-induced defect evolution in monocrystalline silicon [25]. A hybrid Tersoff–ZBL potential was employed to capture the short-range nuclear repulsion and bonding characteristics of silicon under high-energy particle bombardment [26]. The initial simulation cell comprised 10⁶ atoms arranged in a 50a₀ × 50a₀ × 50a₀ lattice (a₀ = 5.43 Å) with periodic boundary conditions, and its lattice structure and configuration are shown in Figure 1a. Figure 1b shows the distribution of Frenkel defects from a perspective perpendicular to the Y-axis, the red marks in the figure indicate vacancies, while the yellow represents interstitial atoms. Figure 1c illustrates the general trend of the entire process from defect generation to stabilization. The simulation cell, comprising 10⁶ atoms, was constructed to accommodate the maximum projected range of primary knock-on atoms (PKAs) at 20 keV and to minimize boundary effects. Prior to irradiation, the system underwent energy minimization using the conjugate gradient algorithm, followed by a 20 ps relaxation in the NVT ensemble at 300 K to achieve a stable equilibrium state with minimized residual stress.

To simulate irradiation damage at the atomic scale, the primary knock-on atom (PKA) method was employed. In this approach, a selected atom in the crystal lattice is imparted with an initial kinetic energy, representing the momentum transfer from an incident energetic particle, thereby initiating a collision cascade. This technique enables the reproduction of defect generation and evolution processes under controlled energetic conditions in molecular dynamics simulations. In the present study, a PKA with an initial kinetic energy of fixed energy was introduced into the simulation cell to replicate realistic radiation conditions. The initial kinetic energy was imparted to a designated PKA atom, and the velocity components were calculated accordingly with the direction set at a 7° angle to the x-axis to avoid channeling effects along low-index crystal directions. The entire simulation process was divided into four stages, totaling 52.4 ps: relaxation (20 ps, 1 fs timestep, NVT); ballistic collision (0.4 ps, 0.01 fs timestep, NVE); defect recombination (2 ps, 0.1 fs timestep, NVE); and stabilization (30 ps, 1 fs timestep, NVE). Ten independent simulations were performed for each condition to ensure statistical reliability.

2.2. Pre-Strain Protocol

To investigate the influence of mechanical loading on radiation-induced defect formation, pre-strain conditions were applied prior to irradiation. Uniaxial strains ranging from −5% to +5% and hydrostatic strains from −2% to +2% were imposed to establish the strain–defect correlations. The mechanical response under these conditions was assessed by monitoring the formation and stability of Frenkel pairs, vacancy clusters, and interstitial distributions.

The cascade evolution during irradiation was delineated into three distinct stages. In the ballistic phase, the PKA transfers its kinetic energy to surrounding atoms, triggering a rapid increase in defect concentration. This is followed by the displacement spike, where high-energy collisions generate localized atomic displacements and promote the formation of defect clusters. In the subsequent thermal spike, the system dissipates excess energy, facilitating defect recombination or the stabilization of surviving defects. The spatial distributions of vacancies and interstitials were quantified using the Open Visualization Tool (OVITO) [27], which revealed the emergence of shell-like defect morphologies under specific pre-strain conditions. The extent of radiation damage was found to be governed by the interplay between the PKA energy and the material’s displacement threshold energy, with higher threshold values corresponding to enhanced radiation tolerance.

2.3. Experimental Equipment and Methods

To validate the simulation predictions, irradiation experiments were performed on monocrystalline silicon specimens. The monocrystalline silicon samples (20 mm × 20 mm × 0.5 mm, <100>-oriented) were irradiated using a Co-60γ-source at a fixed dose rate of 10 kGy/h. In Co-60γ radiation, high-energy photons predominantly interact with Si by Compton scattering, producing a spectrum of energetic electrons that elastically scatter from lattice nuclei. These electron–nucleus collisions generate PKAs with recoil energies up to a few hundred eV—well above the Si displacement threshold—so the ensuing defect production is well represented by our MD simulations that initialize cascades via PKAs. Additionally, dose-to-damage consistency can be established through γ-NIEL/electron-equivalent scaling. For example, a 1.33 MeV Compton electron can transfer up to ${\mathrm{T}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ ≈ 240 eV to a Si atom (Ed ~15–25 eV), which is sufficient to create a PKA and initiate a (sparse) cascade. The distance between the samples and the γ-source was maintained at 25 cm, and the irradiation duration was determined according to the preset total dose and the known dose rate at the sample position, after which the Co-60γ-source was lowered back into the storage pool. A batch-wise timed sampling strategy was adopted to ensure precise dose control. The samples were placed on a sample stage surrounding the source to ensure uniform exposure. After irradiation, the specimens were immediately stored under dry ice conditions to suppress defect annealing, whereas the MD simulations were primarily performed at 300 K for comparison.

Post-irradiation, mechanical properties were characterized via nanoindentation using a Berkovich diamond tip. Nanoindentation tests were conducted at room temperature using a Berkovich diamond indenter. A minimum of five indentations were performed on each sample to obtain statistically averaged values of hardness and reduced modulus. The Oliver–Pharr method was applied to the unloading curves for data analysis. The Young’s modulus and nano hardness were derived from load–displacement curves following the Oliver–Pharr method, which allows for the extraction of hardness and elastic modulus from the obtained curves. This was achieved using the following relation:

$$h_c=h_{max}-\epsilon {\displaystyle \frac{P_{max}}{S}},$$

(1)

where $h_c$ represents the contact depth; $h_{max}$ represents the maximum indentation depth; $P_{max}$ represents the peak load; $S$ represents the unloading stiffness; and $\epsilon$ represents the geometric constant (typically 0.75).

$$S={\displaystyle \frac{dP}{dh}},$$

(2)

where $P$ represents the load, and $h$ represents the indentation depth.

$$A=C_0{h}_c^2+C_1{h}_c+C_2{h}_c^{1/2}+C_3{h}_c^{1/4}+\cdots ,$$

(3)

where $A$ represents the projected contact area.

$$H={\displaystyle \frac{P_{max}}{A}},$$

(4)

where $H$ represents the hardness.

$$E_r={\displaystyle \frac{\sqrt{\pi }}{2\beta }}·{\displaystyle \frac{S}{\sqrt{A}}},$$

(5)

where $E_r$ represents the reduced modulus, $\beta$ is a constant, and $\beta \approx 1.034$.

$${\displaystyle \frac{1}{E_r}}={\displaystyle \frac{1-v_s^2}{E_s}}+{\displaystyle \frac{1-v_i^2}{E_i}},$$

(6)

where $v_s$ represents the Poisson’s ratio of the sample; $E_s$ represents the elastic modulus of the specimen; $v_i$ represents the Poisson’s ratio of the diamond indenter; and $E_i$ represents the elastic modulus of the diamond indenter. Here, $v_i$ = 0.07, $E_i$ = 1140 GPa are the Poisson’s ratio and elastic modulus of the diamond indenter, respectively. Since the Poisson’s ratio of most solid materials falls within the range of 0 to 0.3, the reduced modulus $E_r$ generally serves as a close approximation of the actual elastic modulus.

3. Results and Discussion

The cascade collision process in single-crystal silicon can be divided into three sequential stages: the collision cascade stage, the displacement-thermal spike stage, and the quenching stage [28]. When a PKA collides with a lattice atom, it initiates a series of secondary collisions that propagate until the transferred kinetic energy is exhausted and no additional vacancies are generated. At this point, the concentration of point defects reaches its maximum, corresponding to the vacancy peak. This is accompanied by a localized high-temperature thermal spike, which promotes defect mobility and facilitates recombination.

The temporal evolution of vacancy formation and defect clustering is illustrated in Figure 2, where red spheres denote vacancies and yellow spheres represent interstitial atoms. Four representative snapshots between 0 ps and 32.4 ps are shown. Figure 2a–c capture the initial collision stage, in which the PKA triggers a chain of atomic displacements, causing the defect population to rise sharply and reach the Frenkel pair maximum at the time point in Figure 2c. This is followed by the recombination stage shown in Figure 2c,d, during which vacancies and interstitials accumulate within the high-defect-density regions created during the displacement spike. Their close spatial proximity significantly increases the probability of recombination, leading to a rapid decline in defect density. By the end of the quenching phase, recombination slows and the surviving defects become stable. Spatially, vacancies are predominantly localized near the collision core, whereas interstitial atoms are more widely dispersed. Overall, the observed defect dynamics exhibit the characteristic signatures of cascade collisions in crystalline solids.

Figure 3a presents the TEM image of the non-irradiated sample, showing a uniform surface without discernible defects at a magnification of 0.2 μm. In contrast, after exposure to an irradiation dose of 1000 kGy in Figure 3b, numerous irradiation-induced defects were evident. High-resolution TEM (HRTEM) imaging further revealed that the unirradiated sample shown in Figure 3c possessed a highly ordered lattice, whereas the irradiated sample (see Figure 3d) exhibited pronounced amorphization with the long-range lattice order severely disrupted. This structural degradation was consistent with the MD simulation results, where vacancy and interstitial defects destabilized the lattice, ultimately leading to amorphization. The TEM and HRTEM images in Figure 3 thus serve as a critical direct microstructural validation, visually confirming the lattice disorder predicted by our MD simulations.

The dependence of radiation damage on PKA energy was examined at 1, 5, 10, 15, and 20 keV. As shown in Figure 4a, the number of Frenkel pairs increased nearly linearly with PKA energy in the 5–15 keV range. This trend is consistent with the Kinchin–Pease framework, which links energy deposition to displacement damage, and with predictions from the Norgett–Robinson–Torrens (NRT) model [29]. The NRT estimates are given by the following:

$$N_{NRT}={\displaystyle \frac{0.8E_{PKA}}{2E_d}},$$

(7)

where $N_{NRT}$ represents the number of displacements calculated using the NRT model; $E_{PKA}$ represents the energy of the PKA; and $E_d$ represents the delocalization threshold energy of the material.

Figure 4b compares the simulation results of Frenkel’s defect number under different PKA energies, the NRT model predictions, and experimental data from Zhou et al. [30]. According to the NRT model, the PKA energy and defect number have a linear relationship. The three trends were consistent and the values were close, verifying the reliability of the simulation method used in this paper. Defect morphology evolved significantly with increasing PKA energy. At low energies (e.g., 5 keV), damage remained confined along the PKA trajectory, forming a single defect-rich region. At intermediate-to-high energies (≥10 keV), the cascade fragments into sub-cascades, producing multiple displacement peaks and extending the damage volume. At 20 keV, the morphology became multi-nucleated, with distinct delocalization peaks. In all cases, increasing energy promoted the growth and coalescence of interstitial and vacancy clusters [31]. The cluster fraction, as an important indicator of the degree of defect aggregation, was calculated as follows:

$$f_c={\displaystyle \frac{N_c}{N_t}},$$

(8)

where $f_c$ represents the cluster fraction; $N_c$ represents the number of clusters of defects; and $N_t$ represents the total number of defects of that type.

Based on the calculation of Equation (8), the simulated data were summarized, as shown in

Table 1. Defect cluster fraction at different PKA energies.

PKA Energy (keV)	Vacant Clusters (%)	Interstitial Clusters (%)
1	0.33	0.09
5	0.39	0.28
10	0.32	0.18
15	0.31	0.17
20	0.32	0.17

. No direct correlation with PKA energy was observed, suggesting that clustering is largely governed by intrinsic material properties rather than energy alone. Furthermore, lattice anisotropy introduces incident-direction dependence, influencing both cluster morphology and defect stability [32].

Elevated temperatures markedly extended the initial phase of cascade collisions. As shown in Figure 4c, increasing the irradiation temperature from 100 K to 1200 K prolonged the I-phase [33] due to intensified atomic vibrations, which lowered the displacement threshold and induced additional secondary collisions. This broadened energy transfer pathways and promoted defect generation. Figure 4d further shows that defect recombination rates increase with temperature, which is consistent with suppressed defect clustering. High temperatures significantly reduce the proportion of clusters containing more than three atoms as thermal activation facilitates defect migration, cluster dissociation, and lattice reordering. These processes relieve local stress and hinder the stability of large defect clusters. Temperature also modifies the spatial defect distribution at 100 K and defects remain dense and localized near the collision core, whereas at 900 K, enhanced long-range diffusion of vacancies and interstitials disperses defects more widely, thereby weakening aggregation.

Pre-strain exerts a dual influence in irradiation environments, affecting both lattice geometry and interatomic interactions, thereby modulating defect formation mechanisms. Building on prior simulations, this study systematically investigated the impact of uniaxial and hydrostatic tensile/compressive pre-strains on the defect number, type distribution, cluster morphology, and formation energy in single-crystal silicon. Uniaxial strains were applied along the x-axis, while hydrostatic strains were imposed isotropically. To ensure equivalent volumetric changes, maximum strains of 5% (uniaxial) and 2% (hydrostatic) were selected. Following structural relaxation, a 5 keV PKA was introduced under each condition, with ten independent simulations conducted to ensure statistical robustness.

The results indicate that, under both uniaxial and hydrostatic pre-strains, tensile loading consistently increases both peak and residual defect numbers. Figure 5a,b show a progressive rise in defect counts from compressive to tensile states, with hydrostatic trends exhibiting a milder slope. Figure 5c,d demonstrate a decrease in recombination rates with increasing tensile strain, implying reduced recombination efficiency and greater defect survival. This trend is attributed to lattice expansion, decreased atomic density, and bond relaxation under tension, which collectively enhance Frenkel pair formation. Moreover, tensile strain prolongs collision cascade duration and enlarges the propagation range, enabling more displaced atoms to escape the collision core and stabilize.

Defect analysis shows that interstitials consistently outnumber vacancies across all strain states, as high-energy atoms generated during Frenkel pair formation often remain trapped within lattice interstices. Pre-strain markedly alters both defect clustering and spatial distribution. Figure 6 shows the spatial distribution of defect distributions and cluster evolution under hydrostatic pre-strain that occurred due to the different model sizes caused by pre strain (the model wireframe is not shown in the figure). In Figure 6a,b, the red marks indicate vacancies and yellow represents interstitial atoms. In Figure 6c,d, defects within a certain range were considered as a cluster, and different defect clusters are represented by different colors. At 2% tension, defects were more widely dispersed, with interstitials displaced from the collision core, whereas at −2% compression, defects remained densely localized near the impact center. In tensile states, vacancy clusters predominantly occupy the central region, while interstitials form a peripheral “displacement peak.” This spatial separation suggests that tensile strain promotes vacancy clustering and may facilitate the formation of higher-order defects, such as dislocation loops and voids.

Beyond altering defect quantity and morphology, pre-strain exerts a pronounced influence on Frenkel pair formation energetics. Figure 7 shows that tensile strain significantly elevates interstitial formation energy and widens the energy gap between interstitials and vacancies. Coupled with the observed trends in defect evolution and clustering, these findings suggest that strain concurrently governs collision cascade dynamics, atomic diffusion pathways, and the thermodynamic stability of defects. Tensile strain facilitates defect generation and spatial separation, whereas compressive strain suppresses both processes, highlighting the potential of strain engineering as a strategy to improve radiation tolerance.

To evaluate the influence of defect distribution on mechanical properties, simulations were conducted at a PKA energy of 5 keV with varying initial defect configurations (

Table 2. The defect density, Young’s modulus, yield stress, and yield strain of different PKA energy irradiations.

PKA Energy (keV)	Young’s Modulus (GPa)	Number of Defects	Strain	Yield Stress (GPa)
0	103.02	0	0.47	30.61
1	103.00	26	0.39	26.22
2	102.97	51	0.37	25.14
5	102.90	124	0.36	24.31
10	102.79	248	0.35	23.83

). Five models, containing Frenkel pair concentrations from 0% to 1.0%, were generated by randomly inserting equal numbers of vacancies and interstitials. Following full relaxation using the Nosé–Hoover pressure–temperature ensemble, uniaxial tensile loading was applied to determine the corresponding changes in the Young’s modulus and yield stress.

Figure 8a presents the variation in the Young’s modulus in single-crystal silicon with increasing Frenkel defect concentration. A near-linear decrease was observed, with vacancies exerting a stronger influence than interstitials. Vacancies disrupt atomic coordination, weakening lattice bonds, whereas interstitials generate local stress fields that diminish stiffness. This trend underscores the high sensitivity of the Young’s modulus to crystal integrity. Figure 8b shows the effect of defects on yielding behavior. Both the yield stress and strain decreased nonlinearly with increasing defect concentration. At low concentrations, vacancies and interstitials exhibited comparable effects; however, at higher concentrations, vacancies caused a more pronounced reduction. Nanoindentation experiments were performed to validate the mechanical degradation predicted by simulations. Single-crystal silicon samples, irradiated at a dose rate of 10 kGy/h, were tested using a Berkovich diamond indenter. The unloading stiffness (S) extracted from the load–displacement curve was used to determine the reduced modulus and actual Young’s modulus, as described in Equations (1)–(6). Figure 8c shows that both the nano-hardness and Young’s modulus decreased with increasing experiment irradiation dose, reflecting the accumulation of point defects, vacancies, and dislocations. While our molecular dynamics simulations showed a linear reduction in the Young’s modulus with increasing defect concentration, the experimental data from nanoindentation exhibited a non-linear decrease with increasing irradiation dose. This disparity arose because the simulated single-crystal silicon model had a perfect lattice structure, whereas the experimental samples contained pre-existing manufacturing defects and doping, which influenced the formation and evolution of the irradiation damage. However, the strong qualitative agreement between the simulated and experimental trends in modulus degradation validated the reliability of our MD model and confirmed that the fundamental defect mechanisms captured in the simulation were indeed responsible for the observed macroscopic property changes.

Figure 8d illustrates the effect of Frenkel defects on thermal conductivity (TC). As defect concentration increases from 0% to 0.9%, TC decreases monotonically, with interstitials causing a greater reduction than vacancies. This indicates that interstitials induce stronger lattice distortions, generating localized stress concentrations that enhance phonon scattering. Since TC in single-crystal silicon is dominated by lattice phonon transport, Frenkel defects act as strong phonon scattering centers, reducing the phonon mean free path. At low defect concentrations, TC reduction is primarily governed by elastic scattering, while at higher concentrations, inelastic scattering and nonlinear phonon interactions intensify, leading to a sharp decline and eventual saturation. The observed TC trend parallels that of the Young’s modulus, reflecting the shared underlying sensitivity to lattice disruption. Although thermal conductivity was not directly measured in this study, the strong reduction predicted by MD is supported by both microstructural observations and prior reports. Frenkel defects act as efficient phonon scatterers and, at high concentrations, drive partial amorphization that disrupts coherent transport and shortens phonon mean free paths. This interpretation is consistent with our TEM/HRTEM images showing lattice disorder (Figure 3b,d) and with nanoindentation data indicating defect-induced stiffness degradation (Figure 8c). Moreover, earlier experiments on irradiated silicon have reported comparable TC reductions associated with defect accumulation and amorphization [7,12,13]. Future work will employ Time-Domain Thermoreflectance, 3ω, and suspended-bridge methods to quantitatively validate these predictions.

Following the elucidation of how irradiation-induced microscopic defects (e.g., vacancies and interstitials) lead to a reduction in the Young’s modulus, this study further established a direct link between this microscopic damage and the overall macroscopic performance degradation of the device through macroscopic finite element simulations. It is important to note that our FE model of the silicon diaphragm employs an isotropic approximation for modulus degradation. While single-crystal silicon possesses intrinsic elastic anisotropy, this approximation is justified by several factors. At the device scale, the uniform hydrostatic pressure applied to the diaphragm averages out directional elastic contributions, making an isotropic model a reasonable and computationally efficient approach. Furthermore, the radiation-induced modulus reduction primarily stems from the accumulation of Frenkel defects, a process that inherently disrupts local bonding in a manner that diminishes the relative influence of intrinsic anisotropy on the global response. We acknowledge that, however, for applications with highly anisotropic loading or non-(100)-oriented wafers, incorporating full anisotropic elastic constants in future extensions would be beneficial.

Four representative material states were chosen based on the Young’s modulus retention ratios of 100%, 90%, 80%, and 50%. These ratios correspond to irradiation doses of 0 kGy, 65 kGy, 95 kGy, and 245 kGy, respectively. The elastic properties for each state were then assigned to a three-dimensional FE model of a monocrystalline silicon sensing diaphragm. The model maintained the actual device geometry and boundary conditions. Under a uniform hydrostatic pressure load of P = 45 Pa, we simulated the macroscopic deformation behavior of the diaphragm for different irradiation damage states. The results clearly indicate that, as the Young’s modulus decreased, the diaphragm’s structural stiffness was compromised. Consequently, for a given pressure load, the maximum deformation increased significantly. The maximum indent deformation for pure silicon is 27.20 nm. This value increased to 30.22 nm, 34.58 nm, and—ultimately—54.40 nm as the modulus was reduced to 90%, 80%, and 50% of its original value, respectively. These values were in high agreement with the trend of macroscopic mechanical property degradation observed earlier in this section. Furthermore, the deformation diagram in Figure 9 shows that the decrease in modulus exacerbated the strain localization at the center of the membrane. This nonlinear expansion was closely associated with the spatial separation of defect clusters observed in the MD simulations and the formation of dislocation loops, confirming the mechanism by which microdefect aggregation distorts the local stress field.

This integrated approach directly embeds microstructural defect evolution into device-level performance prediction, avoiding reliance on empirical degradation factors and establishing a physically grounded framework that couples atomic-scale defect dynamics with the macroscopic structural response. Similar attempts have been made in earlier works, where defect-induced property degradation was introduced into continuum-level models; however, those approaches often relied on empirical correction factors or were limited to stress-free samples [6,7,8,9]. In contrast, the present study explicitly coupled MD-predicted defect evolution with FE simulations under realistic loading, thereby offering a more direct mechanistic link. Such a framework underpins structural design, material optimization, and long-term reliability assessment of silicon-based MEMS pressure sensors in radiation environments. The strong agreement between our predictions and experimental observations further aligns with reports of irradiation-induced modulus reduction in silicon-based sensors [6,7], while also highlighting discrepancies with studies suggesting negligible degradation under moderate doses [12,13]. Although the irradiation experiments in this study were conducted at 300 K and under standard atmospheric pressure, realistic reactor conditions involve elevated temperatures and pressures, where defect generation and evolution kinetics differ markedly. High temperatures enhance defect mobility, accelerating annealing and recombination, while high pressures may modify the stability of defect clusters, thereby influencing macroscopic material behavior. Future studies should, therefore, extend experimental validation to reactor-like environments to enable a more comprehensive evaluation of MEMS device reliability and to provide more accurate theoretical guidance for nuclear applications.

4. Conclusions

This study establishes a multi-scale framework directly linking irradiation-induced microstructural damage in monocrystalline silicon to the macroscopic performance of MEMS devices. By integrating molecular dynamics simulations—validated through nanoindentation and TEM—with finite element modeling, we bridge atomic-scale defect evolution and device-level mechanical responses. Results demonstrate that vacancies and interstitials cause measurable stiffness degradation, which amplifies deflection and stress concentrations in sensing diaphragms. This underscores the necessity of incorporating microstructural defect effects into MEMS design to ensure functional stability in radiation environments. Our framework moves beyond empirical models, providing a physics-based tool for predicting device degradation and guiding the optimization of material selection, structural design, and long-term reliability. Importantly, the simulations span 300–1200 K, fully covering reactor-relevant operating temperatures. Elevated temperatures were shown to enhance defect recombination and suppress clustering, which is consistent with expected reactor kinetics. These efforts will enable a more comprehensive evaluation of MEMS reliability in nuclear applications and further strengthen the predictive capability of the proposed framework.