Theoretical Comparison Between Noble Metal (Pd or Ru)-Doped GeS₂ Monolayers as Sensitive Materials upon C₄F₇N Decomposed Gases

Abstract

This work comparably investigates the gas sensing potential of noble metal (Pd and Ru)-doped GeS₂ monolayers upon three C₄F₇N decomposed species (FCN, CF₃CN, and C₂F₄) using the first-principles theory, for operation status evaluation in C₄F₇N-insulated devices. The Pd- and Ru-doping effects on the pristine GeS₂ monolayer are analyzed, followed by the adsorption mechanism and sensing performance of two doped monolayers. Our results demonstrate that while Ru doping induces stronger surface interactions with the GeS₂ substrate and consequently exhibits superior adsorption strengths upon the three gases, the Pd-doped monolayer shows remarkable advantages in charge transfer capability that leads to exceptional room-temperature sensitivity responses of −99.6% (FCN), −95.0% (CF₃CN), and −88.0% (C₂F₄), thus significantly outperforming the Ru-doped system. Combined with the instantaneous recovery for gas desorption, the Pd-GeS₂ monolayer holds significance as an ideal room-temperature sensor to monitor the operation status of C₄F₇N-insulated devices in power systems. This research provides promising insights into the application of GeS₂-based materials for gas sensing in power systems and emphasizes the importance of dopant selection in designing high-performance gas sensing materials, especially for developing advanced electrical equipment monitoring technologies.

1. Introduction

In the global shift toward carbon-neutral energy infrastructure, C₄F₇N-insulated equipment has emerged as a superior eco-friendly substitute for its SF₆-based counterpart, offering comparable dielectric performance while boasting a significantly reduced environmental impact due to its minimal global warming potential [1]. Despite these advantages, the promising insulating medium (C₄F₇N) is susceptible to molecular degradation when subjected to electrical and thermal stresses, including partial discharge, arc discharges, and thermal decomposition. While C₄F₇N-decomposed species, including FCN, COF₂, CF₃CN, and C₂F₄ [2,3], are hazardous, research has identified that these gases can act as indicators of deteriorated insulation in equipment [4]. Crucially, the concentrations of these gaseous species exhibit a direct relationship with both the intensity and progression of insulation defects in C₄F₇N-based apparatus [5]. Consequently, the implementation of workable gas detection methodologies becomes imperative for real-time condition assessment, ensuring operational reliability and extending service life in power distribution systems [6].

Recent breakthroughs in two-dimensional (2D) nanomaterial engineering have revolutionized gas sensing capabilities, with graphene derivatives, transition metal dichalcogenides, and III-V compounds setting new standards for high-sensitivity, energy efficient, and compact detection platforms [7,8,9]. These advanced materials exhibit extraordinary physicochemical characteristics, including exceptional specific surface areas, modifiable electronic band structures, and remarkable sensitivity to ppb-level gases [10,11,12]. Apart from these innovative materials, IV-VI compounds, called group-IV monochalcogenides, (MX₂, M=Ge, Sn; X=S, Se, Te) have attracted particular research interests recently, due to their unique structure and large specific surface area [13,14]. In particular, the GeS₂ monolayer, as a new type of weak interlayer coupling 2D material, is widely investigated in terms of its geometric and electronic properties. It is found that GeS₂ exhibits multiple crystalline phases, and the stable ones include the three-dimensional α-GeS₂ (P3m1 space group) and the layered β-GeS₂ structure (P4m2 space group) [13]. Previous reports show the successful synthesis of 2D GeS₂ nanosheets with thicknesses of up to 1.2 nm, hence paving the way for further exploration into its potential role as a gas sensor [15].

Nevertheless, the practical application of pristine GeS₂ in molecular detection faces inherent limitations due to its weak van der Waals interactions with the target gas species. To address this issue, researchers have developed various modification strategies, with noble metal doping emerging as a particularly effective approach, as proved from the theoretical and experimental investigations [16,17,18]. Recent studies have demonstrated theoretical improvements in gas sensing performance through atomic doping, as evidenced by the enhanced sensitivity and good reusability of a Pd-doped α-GeS₂ monolayer for NO and NO₂ detection [19]. This modification strategy combines the intrinsic advantages of GeS₂ (notably its high charge carrier mobility) with the catalytic properties of metal dopants, positioning doped GeS₂ as a highly promising material for next-generation gas sensing applications [20]. Despite these advances, research on the gas sensing properties of β-GeS₂ monolayers remains largely unexplored. The P4m2 layer group in β-GeS₂ exhibits a distinctive square-lattice arrangement of [GeS₄] tetrahedra [21], creating highly symmetric in-plane atomic configurations and naturally occurring van der Waals gaps that are particularly conducive to gas sensing applications [22]. This unique structural characteristic suggests that metal-doped β-GeS₂ could yield even more pronounced improvements in gas detection performance, making it a compelling subject for further investigation.

Building upon the established efficacy of metal-doped systems, this study employs theoretical methods to examine Pd- and Ru-doped β-GeS₂ (short for Ru-GeS₂ and Pd-GeS₂) monolayers for detecting critical decomposed byproducts of C₄F₇N insulation gas (namely FCN, CF₃CN, and C₂F₄). The selection of Pd and Ru as dopants is based on their well-documented catalytic properties and chemical reactivity from existing theoretical and experimental research, in order to enhance gas adsorption and sensing performances for various nanomaterials [17,23,24,25]. These target gases are chosen for their diagnostic value in insulation condition monitoring: FCN serves as an indicator of partial discharge, CF₃CN signals sever arcing faults, and C₂F₄ emerges during thermal decomposition events [26]. The aims of the first-principles calculations in this work are not only to uncover the modification in the geometric and electronic properties of the GeS₂ monolayer induced by Pd/Ru doping but also to illustrate the gas adsorption and sensing properties of the doped lattice from a theoretical aspect. These analyses can illustrate the importance of metal selection for surface modification, providing a theoretical screening tactic to predict the potential of doped GeS₂ and thus guiding the experimental design of more effective gas sensors tailored for specific industrial needs. Such fundamental understanding is particularly relevant for developing detection systems with improved sensitivity and operational stability. The theoretical framework established in this study demonstrates the considerable potential of GeS₂-based nanomaterials as key components in gas sensing technologies, positioning the MX₂ monolayer as a viable solution for diagnostic applications in high-voltage electrical equipment.

2. Results and Discussion

2.1. Analysis of Pristine GeS₂ Monolayer and Typical C₄F₇N Decompression

The optimized geometric configuration, accompanied by the corresponding band structure (BS) and density of states (DOS) for the pristine GeS₂ monolayer are presented in Figure 1, to provide fundamental insights into its intrinsic properties. The relaxed structure depicted in Figure 1a exhibits the uniform Ge-S bond lengths of 2.26 Å throughout the lattice. The calculated lattice parameters (a = 3.51 Å, b = 4.69 Å) demonstrate agreement with previously reported values (a = 3.53 Å, b = 4.70 Å) [27], with the minor discrepancies (≤0.02 Å) well within the expected range of variation due to differences in basis set selections [28]. The observed consistency between our theoretical results and established findings is particularly significant as it confirms the reliability of our approach for subsequent investigations of doped GeS₂ systems.

The BS analysis in Figure 1b reveals that the GeS₂ monolayer exhibits a direct bandgap of 1.568 eV, with both the conduction band minimum (CBM) and valence band maximum (VBM) located at the Γ point, in accordance with previous theoretical studies confirming its direct semiconductor characteristics [29]. As revealed by the DOS analysis in Figure 1c, the electronic structure shows perfect symmetry between the top and bottom S sub-lattices, as evidenced by the identical DOS profiles for S atoms in both atomic planes. The detailed orbital DOS demonstrates significant hybridization between S 3p and Ge 4p states at multiple energy levels (−4.5, −3.9, −3.1, −2.0, −0.6, 1.8, and 2.3 eV relative to the Fermi level), reflecting the strong covalent character of Ge-S bonds that contributes to the material’s structural stability. Moreover, Hirshfeld population analysis quantifies the charge distribution within the monolayer, revealing a net transfer of 0.244 electrons from Ge to each S atom (Ge: +0.244 e; S: −0.122 e). This charge redistribution is consistent with the relative electronegativities of the constituent elements (S: 2.58; Ge: 2.01) [30], and further confirms the ionic–covalent nature of the chemical bonding in the GeS₂ monolayer.

In addition, a comprehensive evaluation of the structural integrity and thermodynamic stability of the pristine GeS₂ monolayer is conducted through molecular dynamics (MD) simulations (Figure S1) and vibrational frequency analysis. MD simulations spanning 200~600 K confirm that although thermal vibrations induce atomic displacements, the full configuration of the GeS₂ monolayer retains its structural integrity without significant distortion or bond dissociation. Vibrational spectrum analysis reveals exclusively real frequencies (6.71~455.68 cm⁻¹), with the absence of imaginary modes validating dynamical stability [31]. Concurrently, the total energy fluctuated within 0.001 Ha (0.027 eV) throughout 2000 simulation steps, proving the outstanding resilience to thermal perturbations. These collective findings—structural persistence under thermal stress, dynamically stable phonon spectrum, and minimal energy variance—give rise to the compelling evidence of outstanding thermodynamic stability [32]. This robust behavior originates from the strong covalent bonding network that permeates the monolayer’s architecture.

The optimized configurations of three decomposed byproducts of C₄F₇N (FCN, CF₃CN, and C₂F₄) are displayed in Figure 2, in which each gas species contains distinct functional moieties critical for surface interactions. These molecules feature two principal reactive centers: (i) carbon–carbon double bonds (C=C, 1.33 Å) and (ii) cyano groups (C≡N, 1.16 or 1.17 Å), with bond lengths conforming to established values [33,34]. The electron-rich nature of these functional groups, particularly the lone pair electrons on unsaturated C and N atoms, renders them highly reactive on nanomaterial surfaces, serving as primary adsorption sites in our interfacial studies. Furthermore, a comparative analysis of C-F bond lengths reveals significant structural variations (1.28–1.35 Å) across different molecular species, reflecting the electronic impact of adjacent functional groups [35]. This bond length modulation suggests varying degrees of bond polarization and differential chemical reactivity among the decomposed products, which are expected to profoundly influence their adsorption thermodynamics and kinetics on the doped GeS₂ surface.

2.2. Pd- and Ru-Doping Properties Within the GeS₂ Monolayer

To systematically investigate the Pd- and Ru-doping effects, we construct the doped GeS₂ monolayer through atomic substitution, namely by replacing an S atom with a Pd or Ru atom. Such configurations make the metal atom covalently bonded within the 2D lattice, representing a metastable configuration with a significantly higher diffusion barrier. This “anchoring” effect effectively suppresses metal atom migration and aggregation, thereby guaranteeing the long-term structural integrity and consistent performance of the sensor material [36]. The dynamic stability of these doped configurations are evaluated using formation energy (E_form) calculations, defined as [37]

$$E_{\mathrm{form}}=E_{{\text{M-GeS}}_2}-E_{{\mathrm{GeS}}_2}-{\mu }_{\mathrm{M}}+{\mu }_{\mathrm{S}}$$

(1)

where $E_{{\text{M-GeS}}_2}$ and $E_{{\mathrm{GeS}}_2}$ denote the total energies of doped and pristine systems, respectively, while µ_M and µ_S correspond to the chemical potentials of the dopant atoms and the replaced S atoms in their stable bulk phases. For comparison, we also analyze the doping configuration via the dopant adsorption manner, in which a single Pd or Ru atom as well as Pd₂ or Ru₂ dimer are considered, with the optimized configurations shown in Figure S2. Specifically, single Pd or Ru atoms adsorbed on the pristine GeS₂ surface, exhibiting high mobility, and leading to a strong propensity for aggregation and the formation of metallic clusters. This migration compromises the uniformity and stability of the active sites. Furthermore, when a Pd₂ or Ru₂ dimer is adsorbed, the configurations undergo significant geometric distortion. This structural instability not only alters the intended electronic properties of the doping sites but also increases the system’s energy, making it susceptible to reconstruction or decomposition under operational conditions. All these findings highlight the significance of substitutional doping strategy in this work.

The analysis of E_form can uncover critical insights into the doping characteristics of Pd and Ru within the GeS₂ monolayer, with the optimized structures and the related charge density difference (CDD) of these doped systems presented in Figure 3. The calculated E_form values manifest dramatically different doping behaviors upon the two noble metal atoms. Specifically, Pd doping exhibits endothermic properties with a positive value of 0.61 eV, indicating the requirement of substantial energy input in this process [38]; while Ru doping shows strongly exothermic behavior with a negative energy value of −1.69 eV, suggesting spontaneous incorporation of the Ru atom into the GeS₂ lattice under appropriate synthesis conditions [39]. Such a remarkable difference primarily stems from the enhanced surface interactions between the Ru atom and the GeS₂ substrate compared to Pd atom, as quantitatively reflected in their respective E_form values. Further structural analysis reveals additional evidence supporting this conclusion. The optimized Pd-Ge and Ru-Ge bond lengths measure 2.36 Å and 2.32 Å, respectively. Notably, despite Pd having a slightly smaller covalent radius than Ru (1.39 Å vs. 1.42 Å) [40], the observed longer bond length for Pd-Ge compared to Ru-Ge clearly indicates weaker bonding interactions in the Pd-doped system. This structural observation provides direct confirmation of the more stable integration of Ru atoms into the GeS₂ monolayer [41]. Moreover, the CDD distributions reveal significant electron depletion around Pd and Ru dopants, clearly demonstrating their electron-donating properties within the doped GeS₂ lattice. This observation is quantitatively corroborated by the Hirshfeld charge analysis, which shows net positive charges of +0.236 e and +0.068 e for Pd and Ru dopants, respectively. The higher charge value associated with the Pd dopant indicates its stronger electron-donating capability compared to Ru, suggesting more favorable electron redistribution and pronounced modifications in the electronic properties of the Pd-doped system.

The dynamic stability and structural integrity of both metastable Pd- and Ru-GeS₂ monolayers are investigated through molecular dynamic (MD) simulations and vibrational frequency analysis, as exhibited in Figures S3 and S4. The MD trajectories reveal structural preservation throughout the 2000 simulation steps, with only minimal atomic displacements observed around the dopant centers (Pd and Ru) and no significant distortion of the overall monolayer framework. Complementary vibrational analysis identifies characteristic frequency ranges of 19.90~454.25 and 12.11~467.69 cm⁻¹ for the Pd- and Ru-doped systems, respectively, with all modes being real and positive and thus acting as a definitive indicator of dynamical stability [42]. Furthermore, the total energy fluctuations remain constrained within 0.001 Ha (0.027 eV), demonstrating thermal stability that is comparable to that of pristine GeS₂. These analyses confirm the favorable dynamic stabilities of both metastable configurations, strongly suggesting that these doped monolayers can maintain their fundamental electronic and structural properties when subjected to thermal and mechanical stresses. However, the high sulfophilicity of palladium must be considered, as it presents a significant experimental challenge, namely the potential formation of palladium sulfide (Pd_xS_y) phases under sulfur-rich conditions. Therefore, the experimental realization of the proposed Pd-GeS₂ monolayer necessitates precise control over the chemical potential during synthesis. The use of a sulfur-poor atmosphere, for instance, would be essential to suppress the nucleation of bulk sulfides and promote the successful incorporation of isolated Pd atoms into the lattice.

Following the above assumptions, electronic structure analyses through the examination of BS and DOS of Ru- and Pd-GeS₂ monolayers are carried out to provide fundamental insights into the doping-induced electronic modifications, as plotted in Figure 4. Notably, both dopants induce significant bandgap reduction relative to pristine GeS₂, wherein the Pd-doped system exhibits a more substantial bandgap narrowing to 0.582 eV (62.9% reduction), compared to the Ru-doped system’s bandgap of 1.005 eV (27.9% reduction). In addition, both doped systems retain the direct semiconductor character of pristine GeS₂, with the VBM and CBM maintaining their coincident positions in the Brillouin zone (K point for Pd-doped systems and Γ point for Ru-doped systems). However, the largely narrowed bandgap in the Pd-doped system suggests significantly enhanced electrical conductivity compared with the Ru-doped counterpart, as evidenced by the reduced energy barrier for charge carrier excitation [43]. Specifically, the stronger bandgap reduction and enhanced charge transfer characteristics of Pd-doping may be particularly advantageous for gas sensing applications, where improved electrical conductivity can enhance sensitivity [44].

An examination of the DOS data provides critical insights into the electronic modifications induced by Pd and Ru doping in the GeS₂ monolayer. The analysis reveals significant hybridization between the noble metal d-orbitals and Ge p-states, with differences in the energy ranges and intensities of these interactions. Specifically, the Pd 4d-Ge 4p orbital coupling occurs predominantly in two energy windows (−4.4 to −0.1 eV and 0.5 to 2.6 eV), while the Ru 4d-Ge 4p interactions span different ranges (−4.9 to −0.2 eV and 0.8 to 2.5 eV). These hybridization features demonstrate substantial electronic coupling between dopant and host atoms, with the Ru-doped system exhibiting stronger interactions near the Fermi level as supported by broader energy distributions and stronger orbital overlaps [45]. This finding aligns perfectly with the thermodynamic preference for Ru incorporation, as evidenced by its more negative E_form. These newly hybrid states serve as active centers for molecular adsorption while maintaining favorable charge transport properties in doped GeS₂ systems, enabling high-performance surface reactivity and sensing applications [46].

2.3. Gas Adsorptions on Pd- and Ru-GeS₂ Monolayers

This section evaluates the adsorption characteristics of Pd- and Ru-GeS₂ monolayers toward three decomposed gases of C₄F₇N. The adsorption configurations are constructed by positioning each target gas molecule approximately 2.5 Å above the dopant center (Pd or Ru) within the GeS₂ lattice, followed by geometric optimization to determine the most stable configurations (MSCs). The thermodynamic stability of each adsorption complex is quantified through adsorption energy (E_ad) calculations, defined as [47]

$$E_{\mathrm{ad}}=E_{\mathrm{monolayer}/\mathrm{gas}}-E_{\mathrm{monolayer}}-E_{\mathrm{gas}}$$

(2)

where E_{monolayer/gas}, E_monolayer and E_gas represent the total energies of the adsorption complex, the isolated doped monolayer, and free gas molecule, respectively. Such parameters can serve two purposes, including identifying the MSC for each gas–surface system through the most negative E_ad value, and enabling quantitative comparison of adsorption strengths across various gas species. Complementary to the energetic analysis, CDD calculations are also performed for each MSC in the Pd- and Ru-doped systems to elucidate the fundamental nature of gas–surface interactions, including charge transfer pathways and chemical bonding mechanisms at the adsorption interface.

For reference, the adsorption behavior of C₄F₇N and its decomposition products on the pristine GeS₂ monolayer are also investigated, with configurations shown in Figure S5. Calculation via Equation (2) reveals consistently weak interactions for all species, with E_ad values of −0.2 eV for C₄F₇N and −0.12 to −0.21 eV for the decomposition products. These findings demonstrate the inherently low adsorption capability of the pristine GeS₂ monolayer toward the target gases, underscoring its limited potential for direct sensing applications and highlighting the critical need for surface modification to achieve usable sensitivity.

2.3.1. Analysis of Pd-GeS₂/Gas Systems

Figure 5 illustrates the MSC and corresponding CDD for FCN, CF₃CN, and C₂F₄ adsorption on Pd-GeS₂ monolayers. For FCN and CF₃CN systems, simultaneous bond formations occur between the Pd dopant and both C and N atoms, with Pd-C bond lengths of 2.08 Å (FCN) and 2.16 Å (CF₃CN), and Pd-N distances of 2.22 Å in both systems. For the adsorbed C₂F₄ molecule, two C atoms are captured by the Pd dopant forming Pd-C bonds measuring 2.19 Å and 2.20 Å. These structural parameters reveal strong interfacial interactions in all three systems [48], corroborated by the calculated E_ad of −0.98 eV (FCN), −0.88 eV (CF₃CN), and −0.76 eV (C₂F₄). These binding preferences can be attributed to the Pd dopant’s pronounced affinity for π-electron systems, particularly the C≡N and C=C functional groups, through strong π-backdonation effects [49].

Hirshfeld charge analysis quantifies significant electron transfer from the doped monolayer to all adsorbed species, with net charges of −0.197 e (FCN), −0.177 e (CF₃CN), and −0.163 e (C₂F₄). The consistent electron-accepting behavior of the gas molecules highlights the Pd’s exceptional electron-donating capability, facilitating substantial charge redistribution in adsorption. Notably, both E_ad and Q_T follow the same trend across the three systems: FCN > CF₃CN > C₂F₄. Moreover, the CDD plots provide spatial confirmation of these electronic interactions, showing pronounced electron accumulation at all Pd-C and Pd-N interfacial regions. This electron density redistribution, combined with the measured bond lengths and charge transfer values, unequivocally demonstrates the formation of covalent bonds between the Pd dopant and adsorbed molecules [50]. These comprehensive analyses collectively establish the chemisorption nature of all three gas–surface systems, with covalent bonding as the dominant interaction mechanism.

An investigation on BS and DOS of the gas-adsorbed system is conducted to elucidate the electronic modifications in the Pd-GeS₂ monolayer following adsorption of three gas species, as illustrated in Figure 6. The calculations reveal non-magnetic ground states for all configurations, confirmed by the absence of spin polarization in their respective DOS profiles. Notably, gas adsorption induces substantial bandgap reduction relative to the isolated Pd-GeS₂ monolayer (0.669 eV), with the modified bandgaps measuring 0.378 eV (FCN), 0.515 eV (CF₃CN), and 0.560 eV (C₂F₄), representing reductions of 43.5%, 23.0%, and 16.3%, respectively. Such remarkable bandgap modulation exhibits a clear trend (FCN > CF₃CN > C₂F₄) that directly correlates with the adsorption strength established in previous energetic analyses. It should be noted that the observed electronic restructuring stems from two mechanisms: (i) charge transfer between the adsorbates and the monolayer that shifts the Fermi level position, and (ii) interfacial orbital hybridization that reconstructs the band edges. Thus, further orbital DOS analysis is conducted to reveal the basic interactions driving these modifications, implying significant hybridization between Pd 4d-orbitals and C 2p/N 2p states of the adsorbed gases. The DOS decomposition shows particularly strong orbital mixing in all three systems, with C 2p and N 2p states forming new electronic features near the Fermi level through coupling with Pd 4d-orbitals. This interfacial interaction is most pronounced in the FCN system, consistent with its strongest adsorption energy and greatest bandgap reduction. These electronic structure analyses provide fundamental insights into the adsorption-induced property modifications of the Pd-GeS₂ monolayer at the atomic level, establishing its potential as a gas-sensitive 2D candidate [51].

2.3.2. Analysis of Ru-GeS₂/Gas Systems

The MSC and CDD plots for FCN, CF₃CN, and C₂F₄ adsorption on the Ru-GeS₂ monolayer are displayed in Figure 7, which reveals interaction mechanisms analogous to those in Pd-doped systems. Structural analysis shows equivalent coordination in FCN and CF₃CN systems, with Ru-C bond lengths of 2.07 Å and 2.12 Å, and Ru-N distances of 2.18 Å and 2.16 Å, respectively. In addition, the C₂F₄ molecule forms two equivalent Ru-C bonds measuring 2.17 Å. Notably, these interfacial bond lengths are all shorter than the Pd-doped counterparts, suggesting the marginally stronger adsorption interactions in Ru-GeS₂ systems upon three C₄F₇N decomposed gases. The enhanced adsorption strength is quantitatively confirmed by calculated E_ad of −1.06 eV (FCN), −0.99 eV (CF₃CN), and −0.94 eV (C₂F₄), all indicative of chemisorption [52].

Hirshfeld charge analysis reveals consistent electron transfer from the monolayer to the adsorbates, with net charges of −0.158 e (FCN), −0.150 e (CF₃CN), and −0.146 e (C₂F₄). While maintaining the same charge transfer direction as those in Pd-doped systems, these values indicate slightly weaker electron-accepting behavior by gas molecules on Ru-GeS₂ surfaces. CDD analysis demonstrates pronounced electron accumulation at Ru-C and Ru-N regions, verifying the formation of covalent bond formation [53]. Importantly, both E_ad and Q_T magnitude follow identical hierarchical trends (FCN > CF₃CN > C₂F₄) across Ru- and Pd-doped systems, which may suggest a representative gas affinity ordering of noble metal-doped GeS₂ monolayers. These analyses demonstrate comparable but subtly enhanced adsorption performance in Ru-GeS₂ systems, providing valuable insights for dopant selection in designing 2D sensing materials [54].

Figure 8 illustrates a comparative analysis of BS and DOS for gas-adsorbed Ru-GeS₂ systems. Similarly to their Pd-doped counterparts, all three systems maintain non-magnetic ground states, as evidenced by spin-unpolarized electronic calculations. The bandgap evolution reveals a distinct pattern: the original 1.005 eV bandgap of the pristine Ru-GeS₂ monolayer undergoes relatively modest reductions to 0.923 eV (FCN), 0.927 eV (CF₃CN), and 0.951 eV (C₂F₄), representing decreases of only 9.2%, 7.8%, and 5.4%, respectively. This attenuated bandgap modulation follows the same hierarchy (FCN > CF₃CN > C₂F₄) as E_ad and Q_T, mirroring the trend in Pd-doped systems but with a significantly smaller magnitude. These findings indicate the higher sensitivity of the Pd-GeS₂ monolayer for sensing C₄F₇N decomposed gases.

Detailed DOS analysis uncovers substantial electronic reorganization in the Ru-GeS₂ monolayer upon gas adsorption, manifested through pronounced state hybridization near the Fermi level. A closer examination of orbital interactions identifies: (i) distinct coupling peaks at −3.8, −3.2, −1.9, −0.4, and 2.3 eV (N/C 2p-Ru 4d) in the FCN system, (ii) hybridization features at −3.7, −3.2, −2.0, −1.4, −0.5, and 2.5 eV (N/C 2p-Ru 4d) in the CF₃CN system and (iii) interaction peaks at −2.3, −1.3, −0.7, 0.3, 1.0, 2.0, and 2.4 eV (C 2p-Ru 4d) in the C₂F₄ system. These high-intensity hybridizations feature electronic-level evidence for the distinct chemisorption characteristics of the Ru-GeS₂ monolayer [48]. The relatively minor bandgap perturbations in the Ru-GeS₂/gas systems, coupled with localized hybridization peaks, underscore the critical role of dopant selection in determining both the strength and nature of gas–surface interactions in doped monolayers that tailor their sensing properties.

Apart from the above anslyses, a practical gas sensor must exhibit a significant ability to selectively detect trace-level decomposition products in the presence of a high background concentration of the parent gas. To evaluate this critical aspect of selectivity, we systematically investigated the adsorption behavior of the C₄F₇N molecule on both Ru- and Pd-GeS₂ monolayers. Our computational results, summarized in Figure S6, explicitly demonstrate that the interaction between the doped surfaces and the parent C₄F₇N is notably weak, with E_ad values of only −0.36 eV and −0.39 eV for the Pd- and Ru-doped systems, respectively. These E_ad values are indctive of weak physisorption, which typically results in negligible sensor responses [55]. In contrast, the adsorption of key decomposition products, such as FCN, CF₃CN, and C₂F₄, on the same doped surfaces is substantially stronger. This marked disparity in binding strength provides a clear theoretical foundation for high selectivity. The weakly adsorbed parent C₄F₇N molecules are unlikely to persistently block or “poison” the active sites. Instead, these sites remain available for the strong and preferential adsorption of the target decomposition analytes. Consequently, the proposed Ru- and Pd-doped GeS₂ sensors are theoretically capable of distinguishing and detecting critical fault gases within a atmosphere dominated by the parent C₄F₇N.

2.4. Gas Sensor Exploration

The above sections provide a comprehensive investigation on the geometric and electronic properties of gas-adsorbed Pd- and Ru-doped GeS₂ monolayers, which reveals critical structure–property relationships. Specifically, it is demonstrated that while both doped systems exhibit identical hierarchical adsorption strengths for C₄F₇N-decomposed products (FCN > CF₃CN > C₂F₄) that correspondingly lead to similar sequences of bandgap modulation, the Pd-doped configurations display more pronounced electronic modifications. This enhanced responsiveness in Pd-GeS₂/gas systems directly correlates with their greater charge transfer magnitudes, as quantified by Hirshfeld population analysis. These observations establish a clear structure–property paradigm where E_ad determines the relative ordering of bandgap modulation and Q_T magnitude primarily controls the absolute scale of electronic modifications. Also, the bandgap variations have direct consequences for electrical conductivity under gas exposure, as illustrated by the semiconductor transport equation [56]:

$$\sigma =A{e}^{(-B_g/2kT)}$$

(3)

wherein σ represents conductivity, A is charge carrier concentration, B_g represents the bandgap, T denotes the operating temperature, and k is the Boltzmann constant (8.617 × 10⁻⁵ eV/K) [57]. This relationship demonstrates that the adsorption-induced bandgap reductions we observed would lead to exponential increases in conductivity, providing a robust transduction mechanism of engineered 2D materials for sensitive gas detection. As a resistive gas sensor, sensing response (SR) related to electrical conductivity can be quantitatively described by the relationship:

$$SR={\displaystyle \frac{{{\sigma }_{\mathrm{gas}}}^{-1}-{{\sigma }_{\mathrm{pure}}}^{-1}}{{{\sigma }_{\mathrm{pure}}}^{-1}}}={\displaystyle \frac{{\sigma }_{\mathrm{pure}}}{{\sigma }_{\mathrm{gas}}}}-1{=\mathrm{e}}^{\Delta B_{\mathrm{g}}/2kT}-1$$

(4)

with ΔB_g representing the adsorption-induced bandgap shift relative to the isolated monolayer. According to Equation (4), the SR values of two purposed monolayers could be calculated, as depicted in Figure 9.

As illustrated in Figure 9, both Pd- and Ru-GeS₂ monolayers exhibit negative SR values to the three C₄F₇N decomposed gases, though with different sensitivity characteristics. Specifically, the Pd-doped system shows more favorable response magnitudes, achieving SR values of −99.60% for FCN, −95.10% for CF₃CN, and −88.00% for C₂F₄. In comparison, the Ru-doped monolayer demonstrates more moderate sensitivities, with corresponding responses of −79.70%, −78.10%, and −65.10%, respectively. This pronounced performance difference can be attributed to the more substantial bandgap reduction and enhanced charge transfer capability in Pd-doped systems, as evidenced by our previous electronic structure analyses. It should be noted that although both monolayers show limited selectivity upon different decomposed products, it does not diminish their practical utility for insulation-monitoring purposes. This is because in electrical equipment diagnostics, the primary aim is early detection of any decomposition gases as indicators of insulation degradation, rather than the precise identification of specific gas species [58].

All these findings confirm the stronger potential of the Pd-GeS₂ monolayer for monitoring C₄F₇N decomposed species. Apart from that, the dopant selection principle in designing sensing materials can also be established, where the sensitivity of the material could be modulated through choice of noble metal dopant (e.g., Pd versus Ru).

2.5. Recovery Property

Given the outstanding sensing performance of the Pd-GeS₂ monolayer, a thorough comparison of its recovery property with its Ru-doped counterpart becomes imperative to assess its practical viability for repeated detection cycles of C₄F₇N decomposed gases. The material’s recovery property governs its suitability for continuous monitoring applications in electrical equipment, where rapid recovery ensures both sensor reusability and the timely detection of subsequent insulation degradation events. The recovery time (τ) is calculated by employing the van’t Hoff–Arrhenius formalism [59], expressed as

$$\tau =A^{-1}{e}^{(-E_{\mathrm{ad}}/kT)}$$

(5)

where k is the Boltzmann constant (8.617 × 10⁻⁵ eV/K), A represents the attempt frequency (10¹⁶ s⁻¹ [60]), and T is the operating temperature (K). The analysis provides essential insights into the material’s potential for long-term deployment in real-world electrical monitoring applications, where a lower E_ad and higher operating T can largely promote the recovery process.

The computational recovery time of Pd- and Ru-GeS₂ monolayers are exhibited in Figure 10, which uncovers their practical applicability for gas sensing in electrical insulation monitoring. As illustrated in this figure, the Pd-GeS₂ system demonstrates outstanding desorption kinetics at ambient temperature (298 K), exhibiting recovery times of 3.7 s for FCN, 75 ms for CF₃CN, and a remarkably fast 0.71 ms for C₂F₄. These time scales are particularly noteworthy as they fall well within the operational requirements for continuous monitoring systems in power equipment applications. While the Ru-GeS₂ monolayer also shows acceptable recovery characteristics (83.1 s for FCN, 5.4 s for CF₃CN, and 0.8 s for C₂F₄), its performance is notably slower compared to its Pd-GeS₂ counterpart. In other words, the Pd-GeS₂ monolayer is more suitable for gas sensor exploration in comparison with the Rh-doped counterpart.

Consequently, these findings, combining excellent sensitivity with instantaneous recovery, hold significance for intended applications of Pd-GeS₂ as an ideal room-temperature sensor to monitor the operational statuses of C₄F₇N insulated devices. This unique combination of properties enables two critical operational advantages. First, the sub-second recovery times for CF₃CN and C₂F₄ allow quasi real-time tracking of developing fault conditions through rapid sequential measurements [61]. Second, the uniform recovery behavior across different gas species ensures reliable operation regardless of the specific decomposition chemistry. Overall, this work on GeS₂-based material not only paves the way for diagnosing insulation degradation in eco-friendly insulating media, but also emphasizes the importance of dopant selection in designing high-performance gas sensing materials. Future work can particularly focus on bridging the gap between theoretical predictions and practical implementation under continuous operation conditions, to accelerate technological adoption.

3. Computational Details

The first-principles calculations in this study were performed using the DMol³ module [62], employing the generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof (PBE) exchange–correlation functional [63]. To accurately model the weakly interacting systems under investigation, we incorporated empirical dispersion corrections through the DFT-D3 method, which effectively describes van der Waals interactions and long-range electron correlations [64]. The electronic structure calculations utilized a double numerical basis set with polarization functions (DNP), while the treatment of relativistic effects—important for transition metal dopants—was achieved through the density functional semi-core pseudopotential (DSSP) approach [65]. For Brillouin zone integration, a Monkhorst–Pack k-point mesh of 10 × 10 × 1 was employed to ensure convergence in both geometric optimization and electronic structure calculations [66]. Some other parameters were carefully optimized, including an energy convergence threshold of 1 × 10⁻⁶ Ha for self-consistent field iterations, a global orbital cutoff radius of 5.0 Å, and an electronic smearing value of 0.005 Ha [67]. These carefully designed computational protocols ensure the reliable prediction of electronic and adsorption properties for the doped GeS₂ systems. For vibrational analysis, we employed the finite displacement method within the DMol³ framework, constructing the Hessian matrix through numerical differentiation of atomic forces using Cartesian displacements of ±0.015 Å [68]. Additionally, molecular dynamics simulations were performed at 298 K for 2 ps, with a time step of 1 fs to examine the thermal stability of the monolayers [69].

The initial framework was established by constructing an optimized 3 × 4 supercell of the pristine GeS₂ monolayer, comprising 12 Ge and 24 S atoms as its fundamental structural unit. To accurately simulate the 2D characteristics of the system while mitigating artificial periodicity effects, a substantial vacuum spacing of 18 Å was introduced normal to the monolayer plane [70]. For comprehensive electronic structure characterization, we implemented the Hirshfeld population analysis method to quantitatively assess (i) the effective atomic charges of the dopants (denoted as Q_Pd or Q_Ru for Pd and Ru dopants, respectively) within the modified GeS₂ lattice and (ii) the charge transfer (Q_T) in the gas adsorption processes. This approach provides fundamental insights into electronic redistribution, where positive charge values correspond to electron-donating properties of either the metal dopants or adsorbed gas molecules. The resulting charge distribution data offers a crucial mechanistic understanding of the underlying electronic interactions governing the sensing behavior at the atomic scale.

4. Conclusions

Through systematic first-principles investigations, this study presents a comparative evaluation of Pd- and Ru-doped GeSe₂ monolayers for detecting critical C₄F₇N decomposed gases (FCN, CF₃CN, and C₂F₄) in electrical insulation monitoring applications. Our calculations reveal the fundamental differences in metal doping that significantly influence gas sensing performance. While Ru doping demonstrates stronger surface interactions with the GeS₂ substrate (as evidenced by E_f analysis) and consequently exhibits greater adsorption strengths (E_ad = −0.94 to −1.06 eV) compared to Pd-doped systems (E_ad = −0.76 to −0.98 eV), the Pd-doped monolayer surprisingly outperforms in practical sensing metrics. This apparent paradox is resolved through detailed charge transfer analysis, which shows that Pd doping facilitates more substantial electron donation during gas adsorption processes. The enhanced charge redistribution in Pd-GeS₂ translates to exceptional room-temperature SRs of −99.6% (FCN), −95.0% (CF₃CN), and −88.0% (C₂F₄), which largely surpasses the Ru-doped system’s responses of 79.7%, 78.1%, and 65.1%, respectively. Furthermore, the Pd-doped configuration demonstrates superior practical applicability through its instantaneous recovery properties (3.7 s for FCN, 75 ms for CF₃CN, and 0.71 ms for C₂F₄ desorption at 298 K), making it an ideal candidate for real-time monitoring of C₄F₇N-insulated power equipment. These findings not only establish GeS₂-based materials as promising materials for eco-friendly insulation monitoring but also highlight the critical importance of dopant selection in 2D material design, where optimal performance requires the balancing of multiple factors including adsorption strength, charge transfer capability, and recovery kinetics.