Modeling of Chemiresistive Gas Sensors: From Microscopic Reception and Transduction Processes to Macroscopic Sensing Behaviors

Abstract

Chemiresistive gas sensors have gained significant attention and have been widely applied in various fields. However, the gap between experimental observations and fundamental sensing mechanisms hinders systematic optimization. Despite the critical role of modeling in explaining atomic-scale interactions and offering predictive insights beyond experiments, existing reviews on chemiresistive gas sensors remain predominantly experimental-centric, with a limited systematic exploration of the modeling approaches. Herein, we present a comprehensive overview of the modeling approaches for chemiresistive gas sensors, focusing on two critical processes: the reception and transduction stages. For the reception process, density functional theory (DFT), molecular dynamics (MD), ab initio molecular dynamics (AIMD), and Monte Carlo (MC) methods were analyzed. DFT quantifies atomic-scale charge transfer, and orbital hybridization, MD/AIMD captures dynamic adsorption kinetics, and MC simulates equilibrium/non-equilibrium behaviors based on statistical mechanics principles. For the transduction process, band-bending-based theoretical models and power-law models elucidate the resistance modulation mechanisms, although their generalizability remains limited. Notably, the finite element method (FEM) has emerged as a powerful tool for full-process modeling by integrating gas diffusion, adsorption, and electronic responses into a unified framework. Future directions highlight the use of multiscale models to bridge microscopic interactions with macroscopic behaviors and the integration of machine learning, accelerating the iterative design of next-generation sensors with superior performance.

1. Introduction

Gas sensors, which convert information on gas species and concentration into measurable signals, have become indispensable for the detection of various gases in agriculture, environmental safety, industrial processes, and disease diagnosis [1,2,3,4,5,6,7]. Among the various types of gas sensors, chemiresistive gas sensors are advantageous owing to their low cost, simple architecture, good compatibility, and high sensitivity [8,9,10]. Chemiresistive materials typically include metal oxide semiconductors (MOS), two-dimensional materials, conductive polymers, and carbon-based materials [11,12,13,14]. Extensive research has focused on enhancing the performance of chemiresistive gas sensors. These studies primarily concentrate on the development of novel materials, surface modification, and optimization of operating conditions [15,16,17,18,19,20]. Numerous review articles have systematically summarized the experimental approaches for the development of chemiresistive gas sensors [12,21,22,23,24]. It is well recognized that the sensor performance can be fine-tuned over a wide range by varying the materials, fabrication methodologies, dopants, or operation temperature.

While experimental innovations have propelled advancements in chemiresistive gas sensors, a critical gap remains between empirical observations and the sensing mechanisms. The systematic optimization of these sensors also depends on their operational mechanisms [25,26]. Computational modeling is essential for bridging this gap, providing indispensable physical insights into complex gas-solid interface interactions and sensor responses, which are often inaccessible to purely experimental approaches [27,28]. Furthermore, models allow for the prediction of sensor behavior prior to fabrication, significantly reducing the time and cost of sensor optimizations [29,30,31]. Therefore, the modeling of chemiresistive gas sensors is a powerful tool for both advancing the comprehension of the sensing mechanism and accelerating the optimization of gas sensors.

Despite this critical role, existing reviews often treat modeling as ancillary to experimental studies, neglecting the importance of a comprehensive sensing process and mechanism [9]. To date, few reviews have systematically summarized the modeling of chemiresistive gas sensors, with only a limited number of articles summarizing specific modeling approaches [9,32,33,34,35,36]. Given the imperative need to advance the mechanistic understanding and accelerate sensor design, this review comprehensively and critically summarizes the modeling approaches of chemiresistive gas sensors.

The modeling of chemiresistive gas sensors is based on their sensing mechanisms. Chemiresistive gas sensors detect gases based on changes in electrical resistance arising from charge redistribution due to physical/chemical interactions at gas-solid interfaces. Typically, chemiresistive gas sensors rely on receptor function and transducer function to generate responses [37,38,39,40,41]. The receptor function refers to how the sensing materials recognize gas molecules through adsorption or reaction, and the transducer function describes how the sensors convert chemical signals into measurable electrical output. Therefore, to structure this review, we adopt this widely accepted framework of the two fundamental sensing processes, that is, the reception process on gas-solid interfaces and the transduction process translating interaction into resistance changes [24,42,43].

For the reception process, we focus on density functional theory (DFT), molecular dynamics (MD) methods, ab initio molecular dynamics (AIMD) methods, and Monte Carlo (MC) methods. For the transduction process, we primarily introduce band-bending-based theoretical models and power-law models. The applicability and limitations of each model are critically analyzed. Finally, we highlight the Finite Element Method (FEM) as a robust modeling approach for simulating the entire sensing process. An overview of this review is shown in Figure 1.

2. Reception Process

The adsorption and reaction of gas molecules on chemiresistive material surfaces are closely linked to the physicochemical characteristics of the gases and materials [42,44,45]. Key parameters, such as adsorption energy, adsorption configurations, charge transfer between gas molecules and sensing materials, and the density and distribution of surface adsorption sites on the solid, directly govern the sensor performance. Modeling and simulating this complex reception process not only provides mechanistic explanations for experimental observations but also enables data-driven optimization of high-performance sensors by guiding the selection of various parameters. Widely adopted computational models include density functional theory (DFT), molecular dynamics (MD), ab initio molecular dynamics (AIMD), and Monte Carlo (MC) methods.

2.1. Density Functional Theory (DFT)

DFT is a first-principles computational model based on quantum mechanics. The theoretical framework was first proposed by Hohenberg and Kohn in 1964, with its core concept involving the transformation of complex interactions in multi-electron systems into functional problems related to electron density. This theory was later developed by Kohn and Sham into the practical Kohn-Sham equations [46]. With the advancement of computer technology, DFT enables the prediction of electron transfer and redistribution by solving the electron density distributions in many-body systems.

Over the decades, great efforts have been devoted to understanding the behavior of gas molecules on different materials, such as MOS, two-dimensional materials, and carbon-based materials, through DFT calculations. Cui et al. used DFT to study NO₂ adsorption on phosphorene, finding a binding energy of 0.63 eV and 0.21e charge transfer [47]. The interaction between the pz orbitals of NO₂ and phosphorus alters the bandgap and carrier concentration of phosphorene, enabling thickness-dependent performance predictions. Bai et al. investigated the impact of Al doping on the electronic structure of ZnO using a DFT model [48]. They constructed supercell models of pristine ZnO and Al-doped ZnO (Zn₀.₉₃₇₅Al₀.₀₆₂₅O) and calculated their band structures and densities of states. Al³⁺ substitution increases the number of oxygen vacancies, thereby lowering the CO-O⁻ reaction barriers. This modification facilitated electron excitation, significantly enhancing the electrical conductivity of the material. Xia et al. employed DFT to investigate the adsorption of SF₆ decomposition gases on Rh-doped h-BN monolayers, identifying high adsorption energies and significant bandgap modulation upon gas binding. The interaction between gas molecules and the Rh active site alters the electronic structure, revealing strong sensitivity and selectivity toward H₂S, SO₂, SOF₂, and SO₂F₂ [49]. Complementarily, Chen et al. reported that doping SnS₂ monolayers with Pt₃ clusters significantly enhanced their adsorption strength for SO₂ and introduced substantial bandgap variation for SOF₂ and SO₂F₂, making Pt₃-SnS₂ a viable candidate for both gas sensing and capture [50].

Recent studies have increasingly emphasized the importance of experimentally validating DFT predictions to ensure their relevance in real-world sensing applications. For instance, Jain et al. designed a flexible PANI/MoS₂-based NH₃ sensor and used DFT to rationalize the observed gas selectivity, where the charge density difference and Bader charge analysis supported the enhanced interaction with NH₃ molecules [51]. Similarly, Perilli et al. investigated CO adsorption on Co and Ni single atoms embedded in graphene and demonstrated through both DFT and spectroscopic experiments that CO binds preferentially to Co due to the electronic configuration of the metal sites (Figure 2a) [52]. Moreover, the same group validated the sensing mechanism of a NiPc/graphene heterojunction toward NH₃ and NO₂ using a combined DFT-experimental chemiresistive sensing measurements framework, identifying the Ni d_z² orbital as a key player in charge transfer during gas exposure [53].

DFT methods can also be used to guide material preparation. Yang et al. computationally investigated the effects of 12 non-metallic atoms in the environment on anatase TiO₂ (001) and (101) crystal facets [54]. Simulations revealed that F adsorption significantly reduced the surface energy of the (001) facet, enhancing its stability beyond that of the (101) facet while maintaining high reactivity, thereby overturning the traditional thermodynamically dominant facet distribution. Using DFT simulations, Liao et al. demonstrated that NO₂ exhibited the highest adsorption energy and significant charge transfer on the surface of silicon oxycarbide (SiCO)-derived porous carbon among various gas molecules [55]. Additionally, they investigated porous structures with varying C/Si ratios and found that the carbon content critically influenced the specific surface area and pore volume of the porous structures. A recent study by Perilli et al. systematically investigated metal phthalocyanine/graphene (MPc/Gr) interfaces using DFT to reveal how metal centers (Fe, Co, Ni, Cu) and graphene doping levels jointly govern gas sensitivity toward NH₃ and NO₂. This work highlighted the crucial role of the metal d_z² orbital in mediating charge transfer and identified the optimal MPc/Gr combinations for detecting electron-donating and accepting gases with ultrahigh sensitivity [56].

DFT can simulate the formation of chemical bonds, making it an effective tool for explaining complex adsorption mechanisms and pathways as well. For two-dimensional materials and conductive polymers, DFT models directly simulate charge transfer, orbital interactions, and hybridization between target gases and solid substrates, clarifying adsorption configurations and reaction pathways. Shi et al. utilized the DFT model to demonstrate that undoped MoTe₂ primarily exhibited physisorption toward gas molecules, characterized by low adsorption energy, minimal charge transfer, and negligible hybridization in the density of states [57]. In contrast, doping-induced chemisorption significantly enhancs adsorption energy and charge transfer, accompanied by orbital hybridization and chemical bond formation. Similarly, Hou et al. simulated the adsorption behavior of Cl₂, NO, and SO₂ on Cr₃ cluster-doped monolayer GaSe [58]. The gas molecules exhibited significant distortion in their electron cloud structures after adsorption, with chemical bonds forming between Cr atoms and the gases.

For p-type semiconductors, Wang et al. employed DFT to simulate the adsorption behavior of CO, H₂S, and H₂ on the (110) facet of NiO nanoparticles [59]. As shown in Figure 2b, the adsorption energies and bond lengths were calculated, revealing that CO exhibits significantly higher adsorption energy and shorter adsorption distance than H₂S and H₂. This explains the high selectivity of the sensor for CO. Similarly, Wei et al. used DFT to simulate NH₃, H₂, and CO adsorption on the Co₃O₄ (112) facet [60]. It showed exceptional selectivity for NH₃, which was attributed to the exposed unsaturated Co³⁺ sites on the active (112) facet. These sites form strong coordination bonds with the lone pairs of NH₃, resulting in an extremely short Co–N bond length. For n-type semiconductors, Zeng et al. proposed that TiO₂ gas sensors rely on the reaction of pre-adsorbed oxygen with reducing gases [61]. Their simulations showed that oxygen adsorption shifted the valence band to lower energies on the anatase (101) and (001) surfaces, with a larger shift on the (001) facet (Figure 2c). This conductivity reduction serves as the fundamental mechanism for detecting reducing gases. Researchers have also focused on lattice oxygen in gas-sensing mechanisms. Zhu et al. investigated the adsorption behavior of H₂ molecules on SnO₂ (110) surfaces under oxygen-rich and oxygen-free conditions [62]. They found that H₂ preferentially interacts directly with two-fold coordinated lattice oxygen sites rather than through adsorbed oxygen intermediates by comparing the valence band shifts. This work demonstrated that the sensing mechanism of SnO₂-based gas sensors encompasses not only the well-known oxygen adsorption model but also a distinct non-oxygen-mediated adsorption pathway. Lu et al. reported similar findings for CO adsorption via direct lattice oxygen interactions in SnO₂-based gas sensors [63].

Figure 2. (a) Schematic representation of the energy decomposition analysis for the energy contribution of deformation and binding to the adsorption energy of CO (represented as black-red dots) on the Metal(represented as cyan dots)@Gr/Ni surface. Reproduced with permission from Ref. [52]. Copyright 2025 Springer Nature. (b) Adsorption energy configurations of NiO with the (110) facet for (i) CO, (ii) H₂S, and (iii) H₂. (iv) Energy values for NiO with (110) facets for CO, H₂S, and H₂. Reproduced with permission from Ref. [59]. Copyright 2017 Springer Nature. (c) (i) Schematic illustration of the electron transfer process between the adsorbed oxygen and the TiO₂ surface. (ii) Density of states (DOS) for the TiO₂ (101) and (001) surfaces before and after oxygen adsorption. Reproduced with permission from Ref. [61]. Copyright 2010, Japan Institute of Metals.

Figure 2. (a) Schematic representation of the energy decomposition analysis for the energy contribution of deformation and binding to the adsorption energy of CO (represented as black-red dots) on the Metal(represented as cyan dots)@Gr/Ni surface. Reproduced with permission from Ref. [52]. Copyright 2025 Springer Nature. (b) Adsorption energy configurations of NiO with the (110) facet for (i) CO, (ii) H₂S, and (iii) H₂. (iv) Energy values for NiO with (110) facets for CO, H₂S, and H₂. Reproduced with permission from Ref. [59]. Copyright 2017 Springer Nature. (c) (i) Schematic illustration of the electron transfer process between the adsorbed oxygen and the TiO₂ surface. (ii) Density of states (DOS) for the TiO₂ (101) and (001) surfaces before and after oxygen adsorption. Reproduced with permission from Ref. [61]. Copyright 2010, Japan Institute of Metals.

2.2. Molecular Dynamics (MD)

Molecular dynamics (MD) simulation is a modeling approach based on empirical force fields that can simulate the interactions between gas molecules and solids. Compared with DFT, MD neglects quantum effects and struggles to accurately describe the orbital hybridization, charge transfer, and chemical bond breaking/formation. This makes it more suitable for simulating physical adsorption processes that are dominated by van der Waals forces and electrostatic interactions [64,65]. However, MD has lower computational complexity, enabling the simulation of large-scale evolution processes at reduced costs, and is capable of simulating dynamic adsorption systems under temperature- or time-dependent conditions [66,67].

The MD model can calculate key information, such as interaction energies and adsorption configurations, and thereby investigate the influence of material properties on sensor behavior. Min et al. established classical force field models, including the Dreiding model for ZnO lattices and the ThaPPE-EH model for characterizing intermolecular interactions, and systematically analyzed the adsorption kinetics of ethanol and other reducing gases on different ZnO crystal planes using MD [68]. The results demonstrated that the adsorption density distribution peak of ethanol was nearly double that of the other gases (Figure 3a). This reveals the influence of crystal plane orientation on gas-selective adsorption. Geng et al. established models of ZnO with different crystal facets and ZnO@graphene composite materials and employed MD simulations to calculate the physical adsorption energies of NO₂ molecules (Figure 3b) [69]. The results revealed that the introduction of graphene significantly enhanced the adsorption energies, demonstrating that NO₂ molecules were more readily adsorbed on the composite surfaces.

MD simulations can also be used to model adsorption via hydrogen bonding. Huang et al. investigated the adsorption of NH₃ on a flavin mononucleotide sodium (FMNS, C₁₇H₂₀N₄NaO₉P)-modified graphene surface using MD simulations [70]. The phosphate groups in the FMNS molecules served as active anchoring sites that could efficiently adsorb ammonia molecules through hydrogen bonding. As shown in the radial distribution function (RDF) plot (Figure 3c), the interaction distance between NH₃ and phosphorus atoms was quantitatively characterized as 0.39 nm, accompanied by a prominent peak. This indicates the existence of hydrogen bonds between them, as the typical hydrogen bond distances range from 0.2 to 0.4 nm. In contrast, pristine graphene exhibited a low adsorption density due to the lack of active sites.

Some researchers have employed the MD model to investigate the dynamic characteristics of gas-solid interactions, which are challenging to achieve through DFT calculations. MD simulations can operate on nanosecond to microsecond timescales, whereas DFT is typically limited to picosecond-level simulations. Shahabi et al. investigated the adsorption behaviors of CO, N₂O, N₂, and HCN gas molecules on zinc oxide nanotube (ZnONT) surfaces using MD simulations [71]. As shown in Figure 3d(i), HCN exhibited significantly higher contact counts than the other gases over 30 ns. Additionally, the radial distribution function (RDF) of the gas molecules as a function of distance (r) from the ZnONT wall was analyzed (Figure 3d(ii)). The sharp RDF peak for HCN near the nanotube surface further confirmed the most intensive interactions between HCN and ZnONT. Boboriko et al. employed MD simulations to analyze the interaction energies and distribution characteristics of water, hydrogen, methane, and ethanol molecules on the surfaces of TiO₂ and TiO₂:MoO₃ at varying temperatures [72]. The distribution bar charts and heat maps of hydrogen molecule positions at 300 K and 573 K are illustrated in Figure 3e, highlighting the effectiveness of MD in simulating dynamic properties.

Figure 3. (a) The corresponding density distribution profiles for seven gases (CH₃CH₂OH, CH₃OH, CH₃CH₂CH₃, H₂, CH₄, CO, and CO₂) along the z-direction for the (i) (101), (ii) (100), and (iii) (002) crystal planes. Reproduced with permission from Ref. [68]. Copyright 2021 Elsevier. (b) Simulation models for pure (i) ZnO and (ii) ZnO@graphene composite with (110), (002), and (101) facets with NO₂ adsorption after configuration optimization. Reproduced with permission from Ref. [69]. Copyright 2019 Elsevier. (c) (i) Density distributions of FMNS and NH₃ molecules along the x-coordinate in the bare and FMNS models, respectively. (ii) Radial distribution functions (RDF) of the NH₃ molecules as a function of the relative distance to the center of mass of the FMNS molecules in the FMNS model. Carbon, oxygen, nitrogen, hydrogen, phosphorous and graphene were represented as cyan, red, blue, white, tan and yellow dots. Reproduced with permission from Ref. [70]. Copyright 2021 Elsevier. (d) (i) Number of contacts of gas molecules with ZnONT surface. (ii) Comparison of the radial distribution function of gas molecules around the ZnO nanotubes versus distance in the simulation systems. Reproduced with permission from Ref. [71]. Copyright 2017 Springer Nature. (e) Distribution bar chart and heat maps of hydrogen molecule position towards anatase planes towards (100) plane at (i,ii) 300 K and (iii,iv) 573 K. Reproduced with permission from Ref. [72]. Copyright 2021 Elsevier.

Figure 3. (a) The corresponding density distribution profiles for seven gases (CH₃CH₂OH, CH₃OH, CH₃CH₂CH₃, H₂, CH₄, CO, and CO₂) along the z-direction for the (i) (101), (ii) (100), and (iii) (002) crystal planes. Reproduced with permission from Ref. [68]. Copyright 2021 Elsevier. (b) Simulation models for pure (i) ZnO and (ii) ZnO@graphene composite with (110), (002), and (101) facets with NO₂ adsorption after configuration optimization. Reproduced with permission from Ref. [69]. Copyright 2019 Elsevier. (c) (i) Density distributions of FMNS and NH₃ molecules along the x-coordinate in the bare and FMNS models, respectively. (ii) Radial distribution functions (RDF) of the NH₃ molecules as a function of the relative distance to the center of mass of the FMNS molecules in the FMNS model. Carbon, oxygen, nitrogen, hydrogen, phosphorous and graphene were represented as cyan, red, blue, white, tan and yellow dots. Reproduced with permission from Ref. [70]. Copyright 2021 Elsevier. (d) (i) Number of contacts of gas molecules with ZnONT surface. (ii) Comparison of the radial distribution function of gas molecules around the ZnO nanotubes versus distance in the simulation systems. Reproduced with permission from Ref. [71]. Copyright 2017 Springer Nature. (e) Distribution bar chart and heat maps of hydrogen molecule position towards anatase planes towards (100) plane at (i,ii) 300 K and (iii,iv) 573 K. Reproduced with permission from Ref. [72]. Copyright 2021 Elsevier.

2.3. DFT + MD & Ab Initio Molecular Dynamics (AIMD)

Based on the literature reviewed, DFT is particularly strong in atomic-scale calculations but is constrained by small system sizes, while MD specializes in simulating dynamic processes but neglects quantum effects. Given the distinct advantages and limitations of these two models, some articles have proposed a hierarchical integration of both methods to address diverse problems. This hybrid approach leverages DFT to precisely calculate the adsorption energies, transition states, and charge distributions at critical sites, while employing MD to model long-term adsorption kinetic behaviors. This strategy provides comprehensive insights into both the electronic interactions and the temporal evolution of adsorption systems.

Tan et al. employed a DFT model to analyze the adsorption energies, density of states, and deformation charge density of CrB toward the decomposition gases of C₄F₇N (CF₄, C₃F₆, and COF₂) [73]. At the same time, MD simulations were conducted to illustrate the dynamic variations in adsorption energy and adsorption distance of the three gases on the CrB surface within 10 ps, as shown in Figure 4a. These results visually demonstrate the differences in the adsorption stability of the gases on CrB. Wang et al. clarified the adsorption configurations of CO and NO_x gases on ZnO- and TiO₂-doped MoS₂ monolayer surfaces by the DFT model, revealing that doping significantly enhanced material conductivity and selectivity (Figure 4b(i)) [74]. Molecular dynamics (MD) results demonstrated that the energy of the doped system exhibited stable oscillations within a narrow range over time (Figure 4b(ii,iii)), confirming the thermal stability of the doped structure. Similarly, Li et al. utilized DFT to analyze the optimal adsorption sites and electronic interactions of NO, NO₂, and NH₃ on 1T-NbS₂ and 2H-NbS₂ monolayers [75]. They also validated the thermodynamic stability of these materials at 500 K using MD simulations, providing kinetic evidence for the reliability of their sensing performance at high temperatures.

The studies mentioned above represent a simple combination of the two methods without fundamentally addressing their inherent limitations. DFT only provides static information on specific quantum properties, while MD fails to directly correlate dynamic behaviors with electronic evolution. The ab initio molecular dynamics (AIMD) model is capable of describing the dynamic response of electronic structures. By integrating the core principles of first-principles calculations and molecular dynamics, AIMD solves real-time electronic states via DFT at each molecular dynamics iteration step [76,77]. However, the computational cost remains inevitably high.

Some researchers have applied AIMD to simulate dynamic gas adsorption processes on solid surfaces. Zhang et al. investigated the dynamic adsorption mechanism of H₂S gas on the (0001) surface of α-MoO₃ nanobelts using AIMD simulations [78]. The analysis of electronic localization functions (ELF) revealed a two-stage adsorption process. Initially, H₂S underwent physical adsorption via hydrogen atoms interacting with surface O²⁻ ions, which was characterized by non-bonding features (Figure 4c(i)). Subsequently, stable H-O chemical bonds were formed (average bond length: 1.07 Å), with covalent bonding features in the ELF images (Figure 4c(ii)). AIMD simulations visualized the dynamic evolution of electron localization and surface reconstruction, directly linking quantum-scale interactions to macroscopic sensing performance. Choudhuri et al. explored the adsorption mechanisms and stability of NH₃, NO₂, NO, and N₂O on B-, Al-, and Ga-doped graphene surfaces using AIMD [79]. AIMD results showed that B-doped systems exhibited poor selectivity owing to limited charge transfer and small atomic size. Ga-doped systems suffer from structural instability, with elongated Ga-C bonds after adsorption. In contrast, the Al-doped systems maintained constant Al-N and Al-C bond lengths and minimal energy fluctuations during the 5-ps simulations, indicating superior structural stability. Rhrissi et al. further validated the stability of strained and unstrained h-BC₂N monolayers after NO₂ adsorption via AIMD [80]. Simulations at 300 K for 4 ps revealed no bond breaking in either system and minimal potential energy fluctuations, highlighting their structural integrity and robustness. AIMD also confirmed the DFT-predicted NO₂ adsorption distances and adsorption sites, demonstrating strain-enhanced adsorption stability. These findings provide novel insights into the optimization of sensors through strain engineering.

Figure 4. (a) Molecular dynamics calculation of the total system energy of (i) C₃F₆-CrB, (ii) CF₄-CrB, and (iii) COF₂-CrB systems. Reproduced with permission from Ref. [73]. Copyright 2023, MDPI. (b) (i) Top and side views of the most stable configuration of the ZnO−MoS₂ monolayer and its most stable configuration for the adsorption of CO, NO, and NO₂ molecules separately, as well as the total electron density distribution. The total energy and temperature of (ii) ZnO-MoS₂ and (iii) TiO₂-MoS₂ doping systems at 300 K as a function of time. Reproduced with permission from Ref. [74]. Copyright 2024 American Chemical Society. (c) Dynamic evolution process of H₂S on the (0001) surface of MoO₃ from AIMD simulations at 450 K and zero pressure, along with the electronic local functions (ELF). (i) The physical absorption and (ii) the forming of H-O bonding process. The labels S, H, and O represent sulfur, hydrogen, and oxygen atoms, respectively. Reproduced with permission from Ref. [78]. Copyright 2016 Elsevier.

Figure 4. (a) Molecular dynamics calculation of the total system energy of (i) C₃F₆-CrB, (ii) CF₄-CrB, and (iii) COF₂-CrB systems. Reproduced with permission from Ref. [73]. Copyright 2023, MDPI. (b) (i) Top and side views of the most stable configuration of the ZnO−MoS₂ monolayer and its most stable configuration for the adsorption of CO, NO, and NO₂ molecules separately, as well as the total electron density distribution. The total energy and temperature of (ii) ZnO-MoS₂ and (iii) TiO₂-MoS₂ doping systems at 300 K as a function of time. Reproduced with permission from Ref. [74]. Copyright 2024 American Chemical Society. (c) Dynamic evolution process of H₂S on the (0001) surface of MoO₃ from AIMD simulations at 450 K and zero pressure, along with the electronic local functions (ELF). (i) The physical absorption and (ii) the forming of H-O bonding process. The labels S, H, and O represent sulfur, hydrogen, and oxygen atoms, respectively. Reproduced with permission from Ref. [78]. Copyright 2016 Elsevier.

2.4. Monte Carlo (MC)

The Monte Carlo (MC) method, a stochastic simulation approach, is widely applied to model gas adsorption in sensors. Its core principle involves generating numerous possible molecular configurations, accepting or rejecting them based on energy criteria, and statistically analyzing the adsorption behavior. Compared to DFT, MD, AIMD, and MC simulations are computationally efficient and capable of handling systems with millions of atoms [81,82,83]. However, MC cannot capture charge transfer or bond reorganization during chemisorption and relies heavily on predefined parameters (e.g., activation energy and frequency factor), which are typically derived from DFT calculations. Consequently, the accuracy of the MC results directly depends on the precision of the input parameters [84].

MC models are several variants of MC models. Standard MC explores equilibrium properties through random sampling based on the principles of statistical mechanics. However, standard MC should operate in a canonical ensemble (with fixed particle number, volume, and temperature), while gas sensors typically function in open systems, where the external environment continuously introduces gas molecules to the sensors [85]. Consequently, standard MC is unsuitable for simulating gas adsorption on the sensor surfaces. Instead, Grand Canonical Monte Carlo (GCMC) and Kinetic Monte Carlo (KMC) simulations are frequently employed to model gas-solid interactions in sensors. GCMC simulates adsorption equilibria in open systems under the grand canonical ensemble (constant chemical potential, volume, and temperature) [86]. KMC, which is tailored for non-equilibrium dynamic processes, combines the principles of molecular dynamics and MC. Instead of uniform sampling, KMC prioritizes discrete events (e.g., adsorption, desorption, and diffusion) using rate-weighted probabilities to study non-equilibrium kinetic behaviors [87].

GCMC is used to simulate the equilibrium state of adsorption. Gordijo et al. employed GCMC to model the adsorption processes of CO and CO₂ on ZnO surfaces [88]. Simulations were conducted at a constant temperature and varying pressures over 50,000 cycles to statistically calculate the adsorption capacities and molecular distributions. The results, shown in Figure 5a, visually demonstrate monolayer adsorption at low pressures and multilayer adsorption at high pressures. Lithoxoos et al. utilized the GCMC model to investigate the adsorption of multiple gases (N₂, CH₄, CO, CO₂) in single-walled carbon nanotubes (SWCNTs) [89]. Similarly, Bahmanzadgan et al. simulated CO₂ adsorption in SWCNTs with varying diameters using GCMC, as illustrated by the adsorption snapshots in Figure 5b [90]. In small-diameter (8,8) nanotubes, the high curvature enhances the van der Waals interactions, leading to tightly adsorbed CO₂ molecules along the inner walls. In contrast, the larger (20,20) nanotubes exhibited more dispersed molecular distributions. Kowalczyk utilized GCMC to investigate the adsorption and separation of flue-gas components (CO₂, CO, N₂, H₂, O₂, and CH₄) on double-walled carbon nanotubes [91]. Their computational results revealed that CO₂ demonstrated the highest adsorption enthalpy due to its molecular shape matching the pore structure. Consequently, the equilibrium selectivities for equimolar CO₂-X gas pairs exhibited significantly enhanced separation performance under low-pressure conditions.

The simulation of dynamic adsorption processes requires the use of KMC. Skafidas et al. conducted Kinetic Monte Carlo (KMC) simulations to qualitatively explain the role of oxygen in the sensing response of SnO₂-based sensors to CO and H₂O [92]. Pulkkinen et al. later expanded this model by incorporating a broader range of oxygen species [93]. They developed a more comprehensive KMC model based on their previous work on the adsorption/desorption rates of adsorbed oxygen ions [94]. They defined the transition pathways among four species: physisorbed O₂, ionically adsorbed O₂⁻/O⁻, and neutral lattice oxygen (Figure 5c(i)). By employing temperature-dependent reaction rates to describe the kinetic characteristics, the model successfully simulated the changes in the coverage of various oxygen species with temperature (Figure 5c(ii)). Ghosh et al. employed a KMC model to investigate the dynamic adsorption process of N₂ molecules on a monolayer ZnO surface [95]. They first utilized DFT to calculate the adsorption energies and diffusion barriers of N₂ at various adsorption sites, which served as the input parameters for the KMC model. The KMC simulation dynamically tracked adsorption, desorption, and diffusion events after introducing an N₂ flux onto an initially empty surface and revealed that the surface coverage increased with increasing temperature and pressure. Similarly, Le et al. applied KMC to study hydrogen adsorption on a monolayer Sc₂C surface using DFT-derived adsorption and desorption energies as model inputs [96]. Based on the DFT results, they defined permissible and prohibited reactions in the KMC model (Figure 5d). The model accounts for the hydrogen distribution across different layers and dynamic transformation processes. Furthermore, KMC simulations revealed deviations in the AIMD results caused by insufficient simulation timescales, highlighting the advantage of KMC in analyzing long-term kinetic behaviors.

Figure 5. (a) CO distribution density map on ZnO surfaces at (i) 10, (ii) 90, and (iii) 180 bar. Reproduced with permission from Ref. [88]. Copyright 2023 American Chemical Society. (b) CO₂ adsorption snapshots inside SWCNTs of different diameters: (i) (8,8) and (ii) (14,14). Reproduced with permission from Ref. [90]. Copyright 2025 Springer Nature. (c) (i) Model of oxygen exchange at the SnO₂ surface. (ii) The simulated equilibrium coverages of the oxygen species. Reproduced with permission from Ref. [94]. Copyright 2001 Elsevier. (d) Reactions (i) included (arrows) and (ii) prohibited (arrows with cross symbols) in the KMC model. Reproduced with permission from Ref. [96]. Copyright 2020 Royal Society of Chemistry.

Figure 5. (a) CO distribution density map on ZnO surfaces at (i) 10, (ii) 90, and (iii) 180 bar. Reproduced with permission from Ref. [88]. Copyright 2023 American Chemical Society. (b) CO₂ adsorption snapshots inside SWCNTs of different diameters: (i) (8,8) and (ii) (14,14). Reproduced with permission from Ref. [90]. Copyright 2025 Springer Nature. (c) (i) Model of oxygen exchange at the SnO₂ surface. (ii) The simulated equilibrium coverages of the oxygen species. Reproduced with permission from Ref. [94]. Copyright 2001 Elsevier. (d) Reactions (i) included (arrows) and (ii) prohibited (arrows with cross symbols) in the KMC model. Reproduced with permission from Ref. [96]. Copyright 2020 Royal Society of Chemistry.

In summary, DFT, MD, AIMD, and MC models are effective tools for simulating gas-solid interactions in reception processes. The DFT model can accurately quantify charge redistribution and analyze the variation in molecular orbitals and electronic states on material surfaces. MD and AIMD focus on dynamically demonstrating the evolution of adsorption configurations, whereas AIMD can reveal the real-time electronic evolution. MC predicts gas distribution patterns on solid surfaces based on statistical principles. With their assistance, the interaction mechanisms between gases and material surfaces can be understood, which helps guide the optimization of material properties to improve sensor performance. Additionally, modeling this process is of great significance in analyzing the entire sensing mechanism, considering that electron transfer in the reception process is the basis of sensing. In the following section, we discuss the models of the resistance variation of chemiresistive materials induced by adsorption.

3. Transduction Process

Although the reception process governs the initial interaction between gas molecules and the sensing material, these interactions alone do not directly translate into measurable electrical signals utilized in gas sensors. The change in the resistance of the sensing materials caused by electron transfer after gas adsorption is the direct mechanism for gas sensing in chemiresistive gas sensors. The transduction process describes this information transduction process, that is, how the interaction of gas-solid translates into macroscopically measurable electrical signal changes (current/resistance) [35,97,98]. Modeling this process can help reveal the microscopic mechanisms underlying resistance changes. Furthermore, it enables the rapid prediction of response characteristics, thereby reducing the experimental trial-and-error costs.

Commonly used models include band-bending-based theoretical models and power-law models, both of which can be applied to calculate the resistance changes in sensitive materials due to the reception process. The former elucidates the physical mechanisms of charge modulation, and the latter describes the empirical relationships between gas concentration and electrical response. The next section focuses on band-bending-based theoretical models that elucidate how interfacial phenomena modulate the band structure, charge carrier distribution, and, ultimately, the resistance of the sensing materials.

3.1. Band-Bending-Based Theoretical Models

In gas-sensing applications, the band bending of chemiresistive materials changes upon gas adsorption. This alters the surface/interface potential and modulates the carrier concentration or transport pathways, ultimately manifesting as changes in the material resistance [99,100]. This mechanism is currently the most widely accepted theoretical model based on band bending.

For two-dimensional materials, gas adsorption modulates the Schottky barrier height formed at the contact between the metal electrodes and the 2D material. The change in band bending at the metal-2D material interface leads to resistance variation [101,102,103,104,105,106,107]. For n-type MOS materials, an electron depletion layer is formed in the air. When exposed to target gases, gas molecules react with pre-absorbed oxygen anions, releasing electrons into the conduction band. This reduces the potential barrier and decreases the upward band bending at the surface compared to air, ultimately resulting in a thinner depletion layer and lower resistance [108,109,110,111]. For p-type MOS materials, a hole accumulation layer (HAL) is formed in the air. The introduced target gases lead to the release of electrons that recombine with holes, increasing the potential barrier. This enhances the upward band bending at the material surface, reduces the thickness of HAL, and increases the resistance (Figure 6a–c) [112,113]. Changes in band bending are the direct cause of resistance variation, whether at the interface or surface bands.

Figure 6. Schematic of band-bending-based theoretical models based on band bending for (a) 2D materials, (b) n-type MOS materials, and (c) p-type MOS materials. In (b), the gray, red, blue, black and white balls represent Sn, O, adsorbed O, C and H, respectively. The equations O₂→2O⁻ and O⁻→O represent the evolution of oxygen species. Reproduced with permission from Ref. [105]. Copyright 2014 American Chemical Society. Reproduced with permission from Ref. [111]. Copyright 2016, Elsevier. Reproduced with permission from Ref. [113]. Copyright 2020 Elsevier.

Figure 6. Schematic of band-bending-based theoretical models based on band bending for (a) 2D materials, (b) n-type MOS materials, and (c) p-type MOS materials. In (b), the gray, red, blue, black and white balls represent Sn, O, adsorbed O, C and H, respectively. The equations O₂→2O⁻ and O⁻→O represent the evolution of oxygen species. Reproduced with permission from Ref. [105]. Copyright 2014 American Chemical Society. Reproduced with permission from Ref. [111]. Copyright 2016, Elsevier. Reproduced with permission from Ref. [113]. Copyright 2020 Elsevier.

Based on band-bending theoretical models, some studies have qualitatively or quantitatively derived formulas for electrical resistance, which can clearly illustrate the correlation between the resistance of a chemiresistor gas sensor and parameters such as surface potential and carrier concentration. For two-dimensional materials, Liu et al. considered the total resistance as the sum of the channel resistance and contact resistance at the metal electrode/MoS₂ junctions, i.e., R = R_channel + R_contact. Here, R_channel ∝ 1/n and R_contact ∝ exp(φ_SB/kT)/n, where n is the electron concentration in MoS₂ and φ_SB is the Schottky barrier height formed at the MoS₂ electrode junctions [105]. The contact resistance was derived from the thermionic-emission equation. Building on this work, Kim et al. systematically investigated the influence of different electrode materials on the sensor resistance by modifying the Schottky barrier height [106]. Similar characteristics were observed for MoS₂/graphene barristor sensors [107]. They exhibited a widely tunable Schottky barrier height, which could be altered using a back-gate bias. For metal oxide semiconductor materials, Barsan et al. established a theoretical framework based on charge neutrality conditions and Poisson equations in 2001 [35]. Using the band bending-induced potential difference Vs as an intermediary parameter, they derived the relationship between the surface electron concentration n_s and bulk electron concentration n_b: n_s = n_bexp(−qVs/kT). Through geometric constraints and integration, they calculated the depletion layer conductivity and bulk conductivity to obtain the overall sensor conductance. This work provides a theoretical foundation for subsequent studies, enabling formula simplification/modification based on the material depletion status (complete/partial), sensing layer porosity, and so on [108,114,115,116,117,118,119]. The model can be readily adapted for both n-type and p-type materials through parameter/symbol adjustments [114,119]. Subsequent studies on these models have fully discussed how changes in the surface potential and band bending are exponentially translated into resistance variations in the sensing layer. These studies collectively validate the effectiveness of theoretical models based on band bending in predicting the material resistance characteristics.

In many studies on different types of sensors, researchers often draw on the models mentioned above. Through the modification, enrichment, or enhancement of theoretical models, favorable outcomes can typically be achieved. Below is an introduction to models of practical devices inspired by band-bending-based theoretical models, specifically describing the sensor behaviors under changes in material properties, structures, and operating conditions.

Montmeat et al. proposed a three-boundary point “gas-metal-oxide” model to explain the enhanced response of gold-modified SnO₂ sensors [120]. The core of the model was the formation of highly ionized oxygen species (O²⁻) at the three boundary points compared to pure SnO₂ surfaces. These ionized oxygen species induce charge redistribution at the interface, expanding the space charge region and thereby significantly influencing the overall conductivity. Based on this model, they later developed a geometric model of the space charge region to interpret the response mechanisms of SnO₂ thick-film gas sensors (Figure 7a(i)) [121]. Specifically, in air, the resistivity of the depletion zone decreased linearly from the surface (ρ_s) to the bulk material (ρ_m). When the reducing gases were introduced, the depletion zone depth decreased, and the resistivity gradient steepened (Figure 7a(ii)). By treating the material as a series connection of depleted and non-depleted regions, the total conductance can be calculated through piecewise integration based on a band-bending-based model. This model successfully reproduced the experimental decline in the ethanol response with increasing sensor thickness (Figure 7a(iii)).

Andrei et al. developed a model for SnO₂ nanobelt gas sensors with a field-effect transistor (FET) structure and comprehensively described the dynamic modulation of gate electric fields on the conductivity of nanobelts (Figure 7b(i)) [122]. In a hydrogen environment, the gate voltage amplified conductivity changes significantly via the field effect compared to that in air (Figure 7b(ii,iii)), which enhances the sensitivity. Kalinin et al. developed a quasi-1D sensor model for crossed SnO₂ nanowires, attributing the response to cross-junction depletion barriers and metal-nanowire Schottky contacts [123]. Gas adsorption locally modified the junction barrier heights or interfacial carrier transport rather than uniformly affecting the nanostructure (Figure 7c(i)). Additionally, the dynamic field effects of the surface charges were discussed, which caused the time-dependent behaviors and memory effects of the sensor (Figure 7c(ii)). To explain the long-observed phenomenon that the response of SnO₂-based sensors to reducing gases decreases with increasing oxygen partial pressure [99,124], Zhao et al. established a band-bending model to describe the oxygen partial pressure-dependent response of SnO₂-based sensors to CO [125]. Notably, the model predicted that at extremely low oxygen partial pressures, the response would saturate or even decline due to downward band bending (Figure 7d). This result offers critical guidance for optimizing the operating conditions of high-response sensors.

These specific models demonstrate that with the help of a band-bending-based theoretical model, the resistance and response processes of the sensors can be effectively simulated; however, the simulations remain computationally intensive. Furthermore, although they share common sensing mechanisms, practical implementations often require model reconfiguration tailored to individual device architectures, indicating their limited generalizability across diverse sensor structures.

Figure 7. (a) (i) Schematic representation of the space charge area considered for geometrical modeling. (ii) Resistivity distribution in the depleted area relative to the three boundary points (under air (γ = 1, dashed line) and under a reducing gas (γ > 1, solid line)). (iii) Response sensor thickness to ethanol (100 ppm) (points: experiments, with three set of points corresponding to the three sensor production batches, line: model). Reproduced with permission from Ref. [121]. Copyright 2004 Elsevier. (b) (i) Two-dimensional schematic representation of the SnO₂ single-nanobelt FET device used in the simulations. Simulated voltage-current characteristics of the FET device in (ii) air and (iii) 2% hydrogen surrounding atmosphere at room temperature. Reproduced with permission from Ref. [122]. Copyright 2007 Elsevier. (c) (i) Conductometric device based on two crossed quasi-1D nanostructures. (ii) A comparison of the transient response of the wired nanowire top curve and empty pads lower curve to a sudden change of the gate potential from −8.7 to 0 V. Reproduced with permission from Ref. [123]. Copyright 2005 American Institute of Physics. (d) (i) The schematic diagram of conversion dynamics of O₂ and CO. (ii) The response-oxygen partial pressure curve. Reproduced with permission from Ref. [125]. Copyright 2022 American Chemical Society.

Figure 7. (a) (i) Schematic representation of the space charge area considered for geometrical modeling. (ii) Resistivity distribution in the depleted area relative to the three boundary points (under air (γ = 1, dashed line) and under a reducing gas (γ > 1, solid line)). (iii) Response sensor thickness to ethanol (100 ppm) (points: experiments, with three set of points corresponding to the three sensor production batches, line: model). Reproduced with permission from Ref. [121]. Copyright 2004 Elsevier. (b) (i) Two-dimensional schematic representation of the SnO₂ single-nanobelt FET device used in the simulations. Simulated voltage-current characteristics of the FET device in (ii) air and (iii) 2% hydrogen surrounding atmosphere at room temperature. Reproduced with permission from Ref. [122]. Copyright 2007 Elsevier. (c) (i) Conductometric device based on two crossed quasi-1D nanostructures. (ii) A comparison of the transient response of the wired nanowire top curve and empty pads lower curve to a sudden change of the gate potential from −8.7 to 0 V. Reproduced with permission from Ref. [123]. Copyright 2005 American Institute of Physics. (d) (i) The schematic diagram of conversion dynamics of O₂ and CO. (ii) The response-oxygen partial pressure curve. Reproduced with permission from Ref. [125]. Copyright 2022 American Chemical Society.

3.2. Power Law

Particularly for metal oxide semiconductor (MOS) gas sensors, the power law serves as a concise and effective model for describing the relationship between material resistance and gas concentration. As early as 1983, Clifford et al. successfully summarized extensive experimental results into an empirical model, proposing that the sensor response R and the partial pressure of the target gas P follow a power-law relationship: R = aPⁿ [126,127]. In 1987, Morrison analyzed a series of reactions describing the reduction of oxygen to adsorbed O⁻ and its interaction with reducing gases at varying partial pressures (P_R) [128]. They found that the resistance varied as P_R^−0.5 at low P_R, but this trend failed to hold at high P_R. However, these findings were empirically derived and lacked a theoretical foundation. In 2008, Yamazoe et al. theoretically validated the power law by integrating semiconductor depletion theory with surface gas-solid reaction kinetics [129]. In this work, oxygen adsorption was assumed to form O⁻ ions for simplicity. Later, in their 2012 study, they extended the power law model to systems involving two adsorbed oxygen species, O⁻ and O²⁻ [39]. They demonstrated that the receptor function dependent on O²⁻ ions exhibited a linear relationship between resistance and P_O2^1/4, while systems relying on O⁻ showed a linear dependence on P_O2^1/2. Hua et al. proposed an approach based on the Schottky barrier model and the law of mass action to interpret the power-law response of MOS gas sensors [130]. They expressed exponent n as

$$n={\displaystyle \frac{dlnR}{dlnP}}={\displaystyle \frac{dln{N}_t}{dlnP}}\times {\displaystyle \frac{dlnR}{dln{N}_t}}$$

where the two terms correspond to the receptor and transducer functions of the sensor. This formulation clarifies the physical interpretation of the power law and simplifies the calculation process. In subsequent studies, they further revealed that the ratio of the metal oxide grain size to its depletion width modulated the exponent n, indicating a dependence of the power-law response on the dimensions and morphology of the sensing material [131]. This refinement addressed the limitations of the original theory of Yamazoe et al., which assumed that the radii of the oxide particles were much larger than their Debye length [129]. Liu et al. investigated the response characteristics of SnO₂ thin-film gas sensors to H₂S [132]. Their experimental results aligned with the power law model (ΔG ∝ C^1/2). Based on this relationship, they modified the traditional gas diffusion theory by replacing the linear assumption with a nonlinear one and employed a Taylor series expansion to simplify the integration process.

Although the power-law model effectively describes the linear correlation between the logarithm of the response and gas partial pressure within conventional concentration ranges, the responses of real sensors often deviate from linearity at extremely high or low concentrations [133]. At ppm-level concentrations, some studies approximate the sensor responses as linear within narrow concentration ranges using the power law model [134,135], which helps determine the limit of detection (LOD). However, when the gas concentration spans a wide range (e.g., across multiple orders of magnitude), the power-law model struggles to accurately predict the sensor responses without constant adjustment of the exponent n.

4. Entire Process

As reviewed above, although numerous valuable studies have separately modeled these two processes, they fail to fully capture the complete operational workflow of the sensors. Moreover, the correlation between surface adsorption and electrical effects has not been established directly. To address this issue, several analytical and recently developed finite element models have been established.

4.1. Analytical Models

In research conducted during the 1990s, some models simplified the reception process by combining diffusion processes with equilibrium adsorption isotherms. The diffusion-reaction model was developed by integrating simplified adsorption isotherms with a band-bending-based theoretical model. Gardner established a linear diffusion-reaction-based model to predict the electrical conductivity of thick-film SnO₂ sensors assuming that the reaction rate surpassed the diffusion process [136]. This model relies on the assumptions of linear adsorption processes, gas diffusion coefficients independent of concentration, and material homogeneity. This method is only applicable for calculating the material conductivity at low target gas concentrations. In 1993, Srivastava et al. introduced the Freundlich adsorption isotherm to revise the linear adsorption assumption in Gardner’s model [137]. They took the coexistence of physical and chemical adsorption on thick-film surfaces into account. In 2000, Lu et al. proposed a corresponding diffusion-reaction model for thin-film metal oxide semiconductor gas sensors [138]. They derived a differential equation that could be used to describe the effects of time and film thickness on the conductivity. However, because these models simulate the reception process based on linear adsorption assumptions or empirical isotherms, their results often deviate from the actual behaviors, and modeling interactions on complex surfaces such as non-uniform porous structures is challenging.

Recently, some studies have employed appropriate physical parameters as mediators to interconnect the physical principles governing both the reception and transduction processes, thereby establishing analytical models that comprehensively describe the entire workflow of sensors.

Göpel and Schierbaum decomposed the conduction of the sensing layer into three core models: grain boundary barriers, bulk resistance, and electrode contacts [139]. Based on the relationship between band bending and depletion layer resistance, they established various equivalent circuit models that systematically correlated gas adsorption, surface chemistry, and macroscopic electrical signals (Figure 8a). Barsan et al. conducted a systematic review of related work, further emphasizing that error-free interpretation of experimental results using such models required critical analysis of the experimental data [31]. Additionally, they noted that this model was only applicable to bulk or thin-film materials and failed to adequately simulate sensors with nanostructured morphologies (e.g., wires, belts, or tubes) due to the presence of localized states. Nguyen et al. employed Langmuir kinetic adsorption equations to describe the dynamic equilibrium of NO molecule adsorption and desorption rates on ZnO surfaces [140]. Using this model, they explored how the variations in the ZnO film thickness and carrier concentration modulated the resistance. Kumar et al. integrated multiphysics models to develop a numerical framework for describing NO₂ adsorption and response on WO₃ [30]. Specifically, they employed a first-order chemical reaction kinetics model to characterize the dynamic process of NO₂ adsorption and mapped gas concentration changes to real-time conductivity changes using the gas equation of state. Fort et al. linked the adsorption process to conductivity changes using the surface charge density (N_s) as a mediator [29]. Surface charges were generated by the competitive adsorption and ionization of CO and O₂ molecules on the SnO₂ nanowire surfaces. They also investigated the direct influence of temperature on conductivity (G). When the temperature increased abruptly, the rapid change in G was governed by carrier mobility (on a millisecond timescale), while N_s adjusted slowly (on a second timescale) owing to chemical reaction hysteresis. This relationship was quantified as a function of G (T, N_s), which can be used to determine the optimal operating temperature.

4.2. Finite Element Method (FEM)

Although the aforementioned entire-process analytical models can accurately and comprehensively simulate the entire workflow of chemiresistive gas sensors, they involve computationally intensive steps with high complexity in terms of understanding and solving. Moreover, the equations describing the reception and transduction processes are mutually coupled and directly dependent on the gas type and sensing material properties. It is challenging to adapt a single model for simulating different sensors through simple parameter modifications, resulting in poor model generalizability.

The finite element method (FEM) can also be used to simulate the entire sensing process of chemiresistive gas sensors. The core principle lies in discretizing differential equations and solving them through piecewise approximations, transforming continuum problems into computations of a finite number of simple elements [141,142]. Compared to the DFT and MD models, the FEM requires significantly less computational effort. Mature finite element software (e.g., ANSYS, COMSOL, and Abaqus) encapsulates mathematical complexities in the backend, providing users with intuitive interfaces and modular functionalities. This makes them far more accessible to understand and modify than theoretical models. Such tools allow straightforward parameter adjustments to readily predict sensor behaviors under different configurations and operating conditions. Furthermore, FEM bridges atomic-scale phenomena to macroscale behaviors intuitively [27,28,143]. The visualization of the simulation results can help clarify the sensing process and the underlying mechanisms.

Currently, only a few studies have attempted to simulate the sensing process and analyze the response characteristics using FEM. Yaghouti Niyat et al. developed a COMSOL multiphysics model for a SnO₂/rGO gas sensor, coupling gas flow (Navier-Stokes), thermal distribution, and charge transfer (Poisson equation) simulations (Figure 8b(i,ii)) [144]. Instead of directly modeling the gas-solid interaction, they incorporated an experimentally derived transfer function to represent the chemisorption effects. Although this approach successfully matched the steady-state experimental data at 300 K, significant deviations occurred in the transient simulations at elevated temperatures (Figure 8b(iii,iv)). These limitations were attributed to the reliance of the transfer function on interpolated experimental data without underlying microscopic reaction mechanisms (e.g., temperature-sensitive rGO oxidation), compounded by non-ideal experimental factors like gas flow inhomogeneity and temperature irregularities. Grazia Lo Sciuto et al. developed a chemiresistive gas sensor model based on ZnO and graft comb copolymer in COMSOL Multiphysics, simulating the complete workflow from gas injection to sensor response [145]. They employed the fluid flow module to simulate the NO₂ distribution in the chamber using the Navier-Stokes equations (Figure 8c) and calculated the dynamic responses in the Electric Currents module via the Poisson equation. However, this work did not explicitly model the gas adsorption process. Instead, it assumes a uniform gas distribution on the sensor surface and proportional adsorption rates to the local concentration, indirectly integrating the gas-solid interaction into the model.

Guarino et al. proposed a method for simulating adsorption-induced changes in the electronic, electrostatic, and transport properties using FEM [28]. They treated the adsorbed molecules as interfacial traps and characterized NO₂ adsorption through variations in the electron trap concentration on the SnO₂ surfaces. They used Langmuir kinetics to dynamically calculate the adsorption/desorption time constants and steady-state adsorption site density. Based on this, the coupled drift-diffusion and Poisson equations were solved using the finite element method in the Sentaurus TCAD. The electron density redistribution and bending of the conduction band caused by adsorption were calculated, explicitly revealing the formation of a depletion layer (Figure 8c). Thus, the nanowire resistance and sensor response were ultimately computed. This is an insightful study on modeling gas sensors using the FEM. Subsequent research could be directed toward a systematic investigation of the impact of diverse parameters on sensor behavior, fully exerting the potential of FEM models.

Figure 8. (a) Geometric structures, electronic band models, and equivalent circuits describing the electrical behavior. Reproduced with permission from Ref. [139]. Copyright 1995 Elsevier. (b) (i) Distribution of the applied gas passing through the chamber from the top to the bottom base. (ii) Temperature distribution on the surface of the sensor. (iii) Response-concentration graph of the real sensor vs. the simulated results. (iv) Response-recovery time graph of the simulated and fabricated sensors exposed to 5 ppm NO₂ at 60 °C. Reproduced with permission from Ref. [144]. Copyright 2018 Springer Nature. (c) (i) Schematic three-dimensional and cross-sectional views of the nanowire. (ii) Sentaurus TCAD model of the nanowire. Reproduced with permission from Ref. [145]. Copyright 2022 Springer Nature. (iii) Calculated electron density in the nanowire with D = 41 nm at 250 °C and 500 ppm of NO₂. Reproduced with permission from Ref. [28]. Copyright 2022 Elsevier.

Figure 8. (a) Geometric structures, electronic band models, and equivalent circuits describing the electrical behavior. Reproduced with permission from Ref. [139]. Copyright 1995 Elsevier. (b) (i) Distribution of the applied gas passing through the chamber from the top to the bottom base. (ii) Temperature distribution on the surface of the sensor. (iii) Response-concentration graph of the real sensor vs. the simulated results. (iv) Response-recovery time graph of the simulated and fabricated sensors exposed to 5 ppm NO₂ at 60 °C. Reproduced with permission from Ref. [144]. Copyright 2018 Springer Nature. (c) (i) Schematic three-dimensional and cross-sectional views of the nanowire. (ii) Sentaurus TCAD model of the nanowire. Reproduced with permission from Ref. [145]. Copyright 2022 Springer Nature. (iii) Calculated electron density in the nanowire with D = 41 nm at 250 °C and 500 ppm of NO₂. Reproduced with permission from Ref. [28]. Copyright 2022 Elsevier.

5. Model Comparisons

To provide a more intuitive and structured understanding of the various modeling approaches discussed above, this section presents a comparative analysis of different models in terms of their representative features, applicable scales, strengths, limitations, and typical applications. By systematically summarizing these models of reception, transduction, and the entire process, this comparison can help guide researchers in selecting the most appropriate modeling strategy for specific sensors and scenarios.

Table 1. Model comparison table.

Processes	Models	Characteristics				Applications
		Applicable Scales	Computational Complexity	Accuracy	Interpretability
Reception Process	DFT	Atomic scale (Å–nm)	High	High (quantum-level detail)	High (physical meaning clear)	Charge transfer, orbital hybridization, adsorption energetics
	MD	Nanoscopic to mesoscopic (nm–μm)	Medium	Medium (limited by force fields)	Medium	Dynamic physisorption, temperature-dependent behavior
	AIMD	Atomic scale, Short time domain	High	High	High	Real-time electronic evolution during adsorption
	MC	Mesoscopic to macroscopic	Low to medium	Medium (parameter dependent)	Medium	Adsorption equilibrium (GCMC), kinetic evolution (KMC), system-level coverage predictions
Transduction Process	Band-bending-based theoretical models	Nanoscopic	High	High	Medium	Carrier modulation, depletion region estimation, resistance change mechanisms
	Power Law	Macroscopic	Low	Medium	Low	Concentration–response fitting, quick prediction, LOD estimation
Entire Process	Analytical Models	Nanoscopic to device scale	High	Medium to high	Medium	Process coupling, time-dependent response simulation
	FEM	Nanoscopic to system scale	Low	Medium to high	High (visualizable, modular)	Full sensor process simulation (gas flow, adsorption, transport, electrical response)

highlights the key characteristics and applicable scenarios of each model.

For the reception process, density functional theory (DFT) is pivotal for atomic-scale analyses of charge transfer, orbital hybridization, and adsorption energetics. Molecular dynamics (MD) and ab initio molecular dynamics (AIMD) provide insights into dynamic adsorption kinetics and structural evolution, while Monte Carlo (MC) methods statistically simulate equilibrium and non-equilibrium adsorption behaviors. However, these models face inherent limitations: DFT struggles with scalability for large systems, MD lacks quantum precision, and MC relies heavily on empirical parameters. Hybrid approaches (e.g., DFT-MD integration or AIMD) partially address these gaps but demand substantial computational resources.

For the transduction process, theoretical models based on band bending elucidate how gas-induced charge redistribution modulates the barrier height and material resistance. Although effective in explaining sensing mechanisms, these models are computationally intensive and poorly generalizable across diverse device architectures. The power-law model provides a concise framework for predicting sensor responses to gas concentrations; however, it struggles to predict responses across wide concentration spans.

For entire-process modeling, the finite element method (FEM) is notable for its ability to integrate multi-physics phenomena—gas diffusion, adsorption, and electronic responses, into a unified framework. With the help of modular software tools (e.g., COMSOL), FEM shows great potential in bridging atomic-scale phenomena to device-level performance and enables intuitive parameter adjustments for performance prediction. Nevertheless, challenges persist in addressing experimental non-idealities and accurately modeling the reception process.

6. Conclusions and Outlooks

Chemiresistive gas sensors have been considered as indispensable tools for gas detection in diverse applications owing to their cost-effectiveness, high sensitivity, and integrability. Precise modeling of chemiresistive gas sensors not only helps to elucidate their operating mechanisms but also accelerates the optimization process, which is critical for advancing chemiresistive gas sensor technology. This review provides a comprehensive overview of the modeling approaches for chemiresistive gas sensors across the reception, transduction, and entire processes, highlighting their respective advantages, limitations, applicable scales, and guiding roles in understanding the mechanism and optimizing the sensor.

Future research should prioritize multi-scale modeling frameworks that connect quantum-scale interactions with macroscopic sensor behavior. Among the various approaches, the finite element method (FEM) has demonstrated significant potential in bridging the multi-physics interactions involved in sensing, ranging from gas flow and adsorption to charge transport and resistance modulation, within a unified computational environment. The FEM is particularly advantageous due to its intuitive visualization, modular architecture, and adaptability to different sensor configurations and operating conditions.

However, current FEM-based models face critical challenges. First, accurately defining the gas reception process at the atomic scale and capturing the complex physicochemical interactions at the gas-solid interface remain difficult within the FEM framework alone. Second, The effective use of these full-process, full-scale models to accelerate the iterative design cycle of high-performance sensors requires systematic investigation. To overcome the first limitation, future work should explore the integration of atomic-scale modeling methods, such as DFT or AIMD, into the FEM framework. By coupling atomic-level insights with multi-scale modeling, it is possible to enhance the physical fidelity of FEM simulations and establish more accurate links between quantum-scale phenomena and macroscopic sensor behaviors. To address the second challenge and accelerate sensor design, FEM can be integrated with machine learning (ML) holds significant promise. ML algorithms can efficiently explore the vast parameter space (including material properties, structural design, and operating conditions) obtained from FEM models and establish complex mappings between the inputs and sensor performance. This enables rapid performance prediction and facilitates inverse design, that is, the identification of optimal configurations for desired sensing characteristics. Such comprehensive and predictive modeling frameworks, combining multi-scale physics with data-driven optimization, are essential for guiding the rational design, performance optimization, and application-specific tailoring of next-generation chemiresistive gas sensors.