3.1. Structure Analysis
The X-ray diffraction (XRD) pattern was utilized to ascertain the phase and purity of both the SnO
2 and the SnO
2-Fe sensors. The observed peaks in the XRD patterns closely matched the standard values obtained from the JCPDS file no. 41-1455 [
55]. These values correspond to a lattice parameter of a = 4.738 Å and c = 3.187 Å for tin dioxide. The XRD Smart Lab Studio II software identified all diffraction peaks, confirming the rutile-type tetragonal crystal structure (cassiterite) in the SnO
2 and SnO
2-Fe sensors.
Figure 4 illustrates their respective XRD patterns.
Introducing iron (Fe) salts into the synthesis of SnO2 films might potentially affect the crystallography observed in X-ray diffraction (XRD) analysis. The presence of Fe dopants may lead to changes in the crystal lattice structure of SnO2, altering the position and intensity of the diffraction peaks. Additionally, incorporating Fe dopants could influence the width of the peaks in the XRD pattern. This explains that the peaks become broader than the original SnO2 sensor, reflecting changes in crystallite size, strain, or defects within the material.
The XRD software successfully identified all diffraction peaks. The Debye–Scherrer equation was used to estimate average crystallite sizes [
56]:
where l is the X-ray wavelength, b is the full width at half maximum, and q is the corresponding angle. The average size of SnO
2 is 12.9 nm while that of SnO
2-Fe is 24.50 nm. The broadening of XRD peaks is generally associated with smaller crystallite sizes, as described by the Debye–Scherrer equation. However, peak broadening can also result from other factors such as strain, defects, and instrumental effects [
57]. In our study, we observed broader peaks for SnO
2-Fe compared to SnO
2, yet the crystallite size calculated for SnO
2-Fe was larger (24.5 nm) than that for SnO
2 (12.9 nm). This apparent contradiction suggests that the broadening of peaks in SnO
2-Fe is not solely due to smaller crystallite sizes but may also be influenced by additional factors such as strain or defects introduced by Fe
+3 doping. It has been reported that the α-phase of Fe
2O
3 is obtained by annealing the samples at 400 °C [
58]. It is suggested that the peaks of Fe
2O
3 could be in the same region as the SnO
2 peaks. These factors can contribute to the broadening of the diffraction peaks without necessarily indicating a smaller crystallite size. There are two possible options: they crystallize separately, or the iron is within the crystalline structure of the rutile crystal of the SnO
2.
3.2. Superficial Area
Obtaining nitrogen adsorption–desorption isotherms is crucial for characterizing materials’ surface area, porosity, and pore size distribution. The SnO2 sensor exhibits notable surface and pore characteristics, with a specific surface area of 28.73 m2/g. This surface area suggests enhanced reactivity and capacity, making it suitable for applications such as adsorption and catalysis. The pore size distribution analysis reveals a mode pore size of 17.28 nm, indicating a predominant pore size range within the material. This information is crucial for understanding the material’s performance in filtration and gas separation processes. Furthermore, the material possesses a pore volume of 0.11 cc/g, indicating its porosity and capacity for the adsorption and diffusion of gases or liquids.
Figure 5a exhibits H
1-type hysteresis, typically associated with uniform materials with spherical particles. Despite this, SnO
2 shows a complex pore structure. This complexity arises not from the particle shape itself but from how these spherical particles are arranged and packed together. The uniformity in particle shape can lead to varied interparticle spacing, especially when particle aggregation occurs in different manners or under varying synthesis conditions. This aggregation can create diverse pore sizes and shapes, leading to the observed irregular adsorption behavior [
58]. This type of hysteresis loop characterizes materials with cylindrical pore geometry and a certain level of pore size uniformity [
59].
H
1-type is commonly observed in materials composed of compacts of nearly spherical particles arranged in a relatively uniform manner [
60]. The observed variation in the form of the H
1-type loop may be attributed to findings from a prior study where SEM imaging revealed a morphology resembling a forest of randomly oriented flakes. These random pathways are ubiquitous, indicating a substantial number of reactive areas attributable to the high porosity of the material.
Figure 5a (inset) shows the adsorption process as an irregular process ascending and descending every certain period until reaching a peak and then a gradual but constant decay period. The irregular behavior in the plot may be Influenced by the surface morphology and structure of the material. If the material consists of randomly oriented flakes on the surface, it can result in a complex pore structure with irregular adsorption behavior. The irregularities in the plot could be attributed to variations in the accessibility and availability of adsorption sites within the pores, which may differ depending on the orientation and arrangement of the flakes.
The SnO2-Fe sample exhibited a surface area of 17.70 m2/g, indicating a substantial area of exposed surfaces per gram of the sample. The analysis of the pore size distribution revealed a mode pore size of 8.78 nm, suggesting that pores around this size are prevalent within the sample. The presence of pores within this size range could enhance the sample’s performance in applications like gas storage or separation processes. The pore volume was also measured to be 0.05 cc/g, indicating a considerable volume of pores available for adsorption or storage. These results provide valuable insights into the structural properties of the SnO2-Fe sample, which can be essential for understanding its behavior in various applications, such as catalysis, gas adsorption, or materials synthesis.
Figure 5b (inset) depicts the adsorption process. The plot shows the derivative of cumulative pore volume concerning pore diameter. It starts with a steady ascent, indicating the presence of pores of various sizes contributing to the total volume. It peaks at a pore diameter of approximately 5 × 10
−3 nm, emphasizing the predominant pore size or range. Then, it steadily decreases without significant noise, suggesting a decline in the contribution of larger pores to the total volume. This indicates that the material’s pore sizes are distributed in a single peak.
Figure 5b shows H3-type hysteresis, indicative of slit-like pores commonly found in plate-like particles. Despite the presence of a wide range of pore sizes as suggested by the H3 hysteresis, the pore size distribution depicted in
Figure 5b predominantly shows a single peak. This observation can be explained by the dominant pore size formed due to the primary mode of particle aggregation or Fe doping levels, which influences the overall pore structure. Although there is a predominant peak, smaller and larger pores also exist but are less frequent, contributing to the overall complexity of the pore structure. The IV(a)-type isotherm typically exhibits a gradual increase in adsorption at low relative pressures, followed by a sharp rise at higher pressures, indicating the presence of mesopores or macropores within the material [
61]. This suggests adsorption occurring via monolayer formation on the external surface and within smaller pores initially, transitioning to multilayer adsorption within larger pores as pressure increases [
62]. The hysteresis loop type H3 indicates a reversible adsorption–desorption process with a wide range of pore sizes or a complex pore structure [
63]. In type H3, the desorption branch is above the adsorption branch at all relative pressures, suggesting desorption occurs at higher pressures than adsorption, possibly due to capillary condensation within larger pores.
In an ethanol sensor, the IV(a)-type isotherm and hysteresis loop type H
3 would exhibit behavior indicative of efficient ethanol molecule detection. Initially, at low ethanol concentrations, the sensor’s response gradually increases, suggesting adsorption occurring through monolayer formation on the sensor’s surface and within smaller pores. As ethanol concentration rises, the response sharply increases, indicating multilayer adsorption within larger pores. This signifies the presence of mesopores or macropores within the sensor material, facilitating effective ethanol molecule detection [
64]. The hysteresis loop type H
3 reflects reversible adsorption–desorption processes, where even as ethanol concentration decreases, the sensor maintains a signal output, implying the retention of some ethanol molecules within the pores or active sites. The desorption branch above the adsorption branch indicates desorption at higher pressures, likely due to capillary condensation in the pores. These characteristics are vital for the sensor’s precise, long-term detection of ethanol concentrations.
3.3. Morphological Analysis
In our previous work [
7], the SnO
2 films demonstrated a forest-like morphology with randomly oriented flakes, enhancing porosity and reaction areas due to the formation process involving multiple dip-coating cycles and sol–gel synthesis. Similarly,
Figure 6a of the current study shows an SEM image of the SnO
2-Fe sensor, where the fractal and porous characteristics are apparent. The fractures within the metal oxide area are produced through the dip-coating and sintering cycle. The particles appear to be irregularly shaped with sharp edges and angular features, suggesting that the sample may have undergone mechanical fragmentation through manipulation or crystallized in an angular form. The surface of the particles appears rough and porous, which could be beneficial for applications requiring high surface area, such as sensing. The particles seem to be aggregated, forming clusters, likely due to the processing method or the natural tendency of SnO
2-Fe particles to agglomerate. The particles’ high surface area and porous nature can enhance the sensitivity and response time of gas sensors made from this material. The rough surface and high surface area are also advantageous for catalytic reactions, providing more active sites for reactions. The variation in contrast observed in the SEM image of the SnO
2-Fe sample (
Figure 6b) is influenced by several factors related to the sample’s morphology and imaging conditions. The observed contrast differences are primarily due to variations in particle size and the presence of different phases, such as iron oxide. Larger particles or aggregates tend to backscatter electrons more strongly, appearing brighter in the image [
65]. This is influenced by the higher average atomic number of the materials forming these aggregates compared to the SnO
2 matrix. Additionally, factors like particle shape and surface roughness also play significant roles in how electrons are backscattered, further contributing to the contrast variations seen in SEM images.
In the energy-dispersive X-ray spectroscopy (EDX) image of the SnO
2-Fe sample, the variations in brightness correspond to differences in the concentration and distribution of elements within the material [
66]. In
Figure 6c, brighter regions in the elemental maps indicate areas with higher concentrations of specific elements. For example, in the tin (Sn) map (
Figure 6d), the brighter areas signify regions with a higher density of tin, likely representing SnO
2-rich areas. In the oxygen (O) map (
Figure 6e), brighter regions correlate with higher oxygen content, which may align with regions of concentrated SnO
2 or other oxides. Similarly, in the iron (Fe) map (
Figure 6f), the brighter regions indicate higher iron concentrations, suggesting iron-rich phases or pure iron areas.
The SEM analysis reveals variations in brightness, suggesting compositional heterogeneity at a microscale within the sample. These variations highlight regions where iron might appear more concentrated or prevalent due to local differences in particle size, shape, or aggregation. Conversely, the EDX analysis provides a broader perspective, indicating that iron is homogeneously distributed within the SnO2 matrix across the entire sample. This uniform distribution, suggesting excellent diffusion behavior, ensures that there are no significant concentrations or deficiencies of iron throughout the material. Such a homogeneous dispersion of iron is beneficial for the performance of SnO2-Fe composites as gas sensors. The even distribution of iron atoms enhances the material’s sensitivity and response time by providing uniformly dispersed active sites for gas interaction, thus ensuring consistent and reliable sensor performance.
3.4. Gas Sensing Experiment
The experiment was conducted as follows: the equipment was run for three and a half minutes with only room air to obtain a stable signal. Then, alcohol vapors and room air were mixed in a small chamber and introduced into the testing chamber, allowing the mixture to flow for three minutes. Subsequently, the flow of ethanol vapors was stopped, and only air was allowed to flow for five minutes to achieve de-saturation. This cycle was repeated up to four times for each of the three runs to observe signal repeatability, resulting in a total of twelve curves for each combination of temperature and concentration.
This data acquisition process was applied to both sensors under the same conditions to allow for comparison. After four reversible cycles, signal data were acquired. To compare the operational work in these new batches of sensors, resistance in air and gas was measured.
Table 1 shows the gas response of the SnO
2 sensor at different temperatures and concentrations. The sensitivity of the sensor was systematically investigated by analyzing its gas response values (S), defined as the ratio of resistance in dry air (Ra) to resistance in the presence of gas (Rg) in reducing gases such as ethanol [
67]. It should be noted that, for convenience, the signal was flipped in our measurements, which means that Rg appears higher than Ra. The data indicate a general trend of increasing sensitivity with both temperature and gas concentration, though some deviations from this trend were observed.
The general trend observed across the data indicates that the SnO2 sensor’s sensitivity improves with increasing temperature and gas concentration. This suggests that the sensor becomes more efficient and responsive at higher temperatures and higher gas concentrations. The highest sensitivity values recorded at 120 °C indicate that the sensor’s optimal temperature for maximum sensitivity lies in this range. The consistent increase in sensitivity with gas concentration at all tested temperatures indicates that the SnO2 sensor can effectively differentiate between different levels of gas presence. This is crucial for applications requiring precise gas detection and quantification.
At first glance in
Table 2, the observation that the resistance in the air is more stable in the SnO
2-Fe sensor compared to the undoped SnO
2 sensor implies that the presence of Fe dopant may influence surface phenomena. This stability suggests that the Fe dopants alter the surface chemistry of the SnO
2 material, leading to enhanced stability in the presence of air. One possible mechanism through which this stabilization occurs is the promotion of oxygen adsorption on the surface of the SnO
2-Fe sensor by the Fe dopants, forming a more stable oxide layer. This stabilized oxide layer could contribute to the consistent resistance observed in the air.
The data also indicate that the SnO
2-Fe sensor exhibits different sensitivity characteristics than the undoped SnO
2 sensor, with notable implications for practical applications. In
Figure 7a, the SnO
2-Fe sensor shows higher sensitivity at lower temperatures (80 °C) and reduced sensitivity at higher temperatures (100 and 120 °C), suggesting that Fe doping alters the temperature response of the sensor. This contrasts with the undoped SnO
2 sensor, demonstrating increased sensitivity at elevated temperatures. The reduced sensitivity of the SnO
2-Fe sensor at higher temperatures may be due to enhanced ethanol desorption, leading to a diminished interaction with the sensor surface. Consequently, the SnO
2-Fe sensor may be more suitable for applications requiring lower operating temperatures, while the undoped SnO
2 sensor is better suited for high-temperature environments where maximum sensitivity is critical; these findings underscore the importance of selecting the appropriate sensor material and operating conditions based on the specific requirements of the gas detection applications.
The graph comparing the sensor response of SnO
2 and SnO
2-Fe sensors to ethanol gas at 120 °C across various concentrations in
Figure 7b reveals significant differences in their performance. The SnO
2 sensor exhibits a constant, low response of around 10 across all ethanol concentrations, indicating minimal sensitivity to ethanol concentration changes at 120 °C. In contrast, the SnO
2-Fe sensor shows markedly higher sensitivity, with the response increasing with ethanol concentration up to 20 ppm, peaking around 50, and then slightly decreasing at 40 ppm.
Figure 7c illustrates the gas response of SnO
2 and SnO
2-Fe sensors to ethanol gas at 120 °C over time, highlighting the enhanced ethanol sensing performance of the Fe-doped SnO
2 sensor. The SnO
2 sensor exhibits a relatively low and stable response of 7.2 to 40 ppm of ethanol, indicating minimal sensitivity to ethanol at this concentration and temperature. In contrast, the SnO
2-Fe sensor shows a significantly higher response to 1 ppm ethanol, reaching peaks at around
kΩ, demonstrating substantial sensitivity even at much lower ethanol concentrations compared to the SnO
2 sensor. The response pattern of the SnO
2-Fe sensor, characterized by periodic peaks and troughs, indicates a strong and consistent response to repeated ethanol exposure.
The Fe-doped SnO
2 sensor’s high sensitivity at low ethanol concentrations and robust and repeatable performance underscores its superior ethanol detection capabilities. The sharp rise and fall of the sensor’s response peaks suggest a quick reaction to ethanol exposure and rapid recovery when the gas is removed, which is crucial for real-time monitoring applications. The SnO
2-Fe sensor demonstrates exceptional ethanol sensing performance across various concentrations (1, 5, 10, and 20 ppm), significantly outperforming the undoped SnO
2 sensor. In
Figure 7d, at 1 ppm, the SnO
2-Fe sensor exhibits a substantial response, indicating high sensitivity even at very low concentrations. This sensitivity remains robust at 5 and 10 ppm, showcasing its reliability and consistent performance. At 20 ppm, the sensor achieves peak response, underscoring its efficiency in detecting moderate ethanol levels.
Response and recovery times (t
res and t
rec) are key parameters in gas sensor assessment. Response time indicates how quickly a device detects a target compound, influencing its responsiveness [
68]. Conversely, recovery time reflects the system’s readiness for repeated measurements, vital for assessing sensing-system throughput, especially in medical and agrifood screening analyses [
69]. Analyzing the SnO
2 sensor response and recovery time to ethanol detection in
Table 3 reveals important insights into its functionality. As the operating temperature increases, the sensor’s response time improves, thereby detecting ethanol more quickly. However, higher temperatures also lead to longer recovery times, indicating the sensor takes more time to reset and be ready for the next detection. The ethanol concentration affects recovery time more noticeably than response time, but its impact is less significant than temperature changes. The sensor is most effective for rapid detection at higher temperatures, though there is a trade-off with slower recovery. These findings highlight the importance of selecting an optimal operating temperature to balance quick detection and efficient recovery, ensuring reliable performance for practical applications.
Then, the data regarding the SnO
2-Fe sensor’s response and recovery times to ethanol detection in
Table 4 unveil its operational characteristics. Unlike the SnO
2 sensor, the SnO
2-Fe sensor exhibits consistent response times across different temperatures and ethanol concentrations, indicating a robust and less temperature-sensitive performance. The response time remains relatively stable at 80 °C, suggesting the sensor can detect ethanol regardless of environmental conditions.
Similarly, the recovery time of the SnO2-Fe sensor shows minimal variation, implying its resilience to changes in ethanol concentration and operating temperature. This stability in recovery time underscores the sensor’s capacity to swiftly return to its baseline state after exposure to ethanol, ensuring a dependable and predictable response in successive detection cycles.
These features imply that the SnO
2-Fe sensor is highly effective for detecting low ethanol concentrations, making it suitable for breath analyzers, industrial safety, and environmental monitoring applications [
70]. The rapid response and recovery times further enhance its suitability for dynamic sensing environments where quick detection and reset cycles are needed. Overall, the significant improvement in ethanol sensing performance due to Fe doping highlights the potential of SnO
2-Fe sensors for advancements in gas sensing technologies, offering precise and reliable detection compared to undoped SnO
2 sensors.
To enhance the response and recovery times of SnO
2 and SnO
2-Fe sensors beyond temperature adjustments, several alternative strategies can be considered. Surface functionalization with catalytic nanoparticles such as platinum (Pt) or palladium (Pd) can accelerate the adsorption and desorption processes of molecules on the sensor surface [
71]. Developing sensors with nanostructured morphologies, such as nanowires, nanotubes, or nanosheets, can increase the surface area and enhance gas diffusion, leading to faster interactions between the gas molecules and the sensor surface [
72]. Additionally, doping with other elements such as cobalt (Co), nickel (Ni), or copper (Cu) can create more active sites and improve the electronic properties of the sensors, facilitating quicker response and recovery [
73]. Light activation using ultraviolet (UV) or visible light can enhance the desorption of gas molecules, thereby reducing recovery times and increasing sensitivity [
74]. Implementing a pulsed voltage rather than a constant voltage can periodically refresh the sensor surface, promoting quicker adsorption and desorption cycles [
75]. Finally, optimizing the sensor design by reducing the thickness of the sensing layer or improving the porosity can enhance gas diffusion and reaction rates, leading to faster sensor dynamics. These strategies offer promising avenues for further improving the performance of SnO
2 and SnO
2-Fe sensors.
Table 5 summarizes the sensitivities, concentrations, operating temperatures, response times, and recovery times for different sensor materials, including SnO
2 and SnO
2-Fe from this work. In comparison to other materials documented in the literature, the SnO
2 sensor from this study demonstrates a moderate sensitivity of 7.2 at 40 ppm and 120 °C, with a response time of 47 s and a recovery time of 272 s for ethanol detection. While these values are respectable, they do not outperform certain advanced materials like SnO
2-CdS, which exhibits an exceptionally high sensitivity of 130 at 100 ppm and 200 °C, with a shorter recovery time of 3 s. Additionally, rGO/SnO
2 shows a significantly higher sensitivity of 48.4 at 50 ppm and 120 °C. However, the recovery and response times for rGO/SnO
2 are not provided, making a complete comparison challenging. Despite these comparisons, the SnO
2 sensor in this study provides a balanced performance with good sensitivity and reasonable response and recovery times, making it a viable candidate for ethanol detection.
The SnO2-Fe sensor developed in this study stands out by demonstrating substantial improvements in sensitivity and response characteristics compared to the undoped SnO2 sensor and other materials in the literature. The SnO2-Fe sensor achieves a sensitivity of 21.7 at just 1 ppm and 80 °C, indicating a remarkable enhancement due to Fe doping. This sensor also exhibits a response time of 73 s and a recovery time of 214 s, which are competitive with other advanced materials. For instance, In2O₃@SnO2 shows a slightly higher sensitivity of 22.6 at 100 ppm and 320 °C but with a faster response time of 1 s and a recovery time of 132 s. The γ-Fe2O₃/SnO2 sensor, while operating at 160 °C, has a lower sensitivity of 5.0 at 100 ppm but benefits from shorter response and recovery times of 25 and 11 s, respectively. Overall, the SnO2-Fe sensor developed in this study offers a significant advantage in terms of sensitivity at lower concentrations and lower operational temperatures, making it highly suitable for practical ethanol sensing applications.
3.5. Mathematical Model
In typical metal oxide sensors (MOX), the detection mechanism involves several key steps: the diffusion of the target gas molecules to the sensor surface, the adsorption of these molecules onto active sites, a chemical reaction occurring at the surface, the desorption of the reaction products, and subsequent diffusion away from the sensor [
82]. This behavior has been accurately described in mathematical models applied to these MOX sensors and put into four stages to imitate the olfaction system [
83]. However, the unique structure of the sensors developed in this study, which incorporate a porous medium and layers of flakes, necessitates a different behavior in these steps. The intricate morphology of these film sensors, characterized by high porosity and layered flakes, alters the pathways and dynamics of gas diffusion, adsorption, and desorption. Consequently, a more complex mathematical model is required to accurately capture the sensor’s response, considering the enhanced surface area and the multilayered structure that influences the interaction between gas molecules and the sensor material.
The schematic in
Figure 8 depicts the complex processes of diffusion and chemical reactions within a detailed porous medium, characterized by a fractal-like structure. As gaseous ethanol interacts with the film surface, it can decompose into various subproducts through interactions with active regions occurring simultaneously within the sensor. Once ethanol molecules are adsorbed onto the active sites, the sensor achieves a steady state. Previous research has suggested that in such complex porous media, anomalous diffusion with adsorption in a fractal dimension is likely to occur [
84]. These phenomena have been extensively explored, with various scenarios proposed, including the introduction of a logarithmic diffusion equation tailored for porous media that incorporates a time-dependent source term [
85]. Consequently, to accurately model the behavior of the SnO
2 and SnO
2-Fe film sensors, it is essential to conduct a thorough analysis of these processes, considering the sensor as a complex porous medium.
The equation governing the change in concentration
is
Thus, the solution of Equation (6) is
where
where
and
are related to the diffusivity coefficient that changes with time and position and
is related to time. On the other hand, the source term could be considered for this research as the changing concentration of ethanol on the surface sensor:
this change in concentration is due to the oxidation of ethanol, assumed to be a first-order reaction where
is the initial concentration of ethanol:
therefore,
this changing concentration in Equation (11) can be related to the consumption of electrons at the surface used to decompose ethanol into its subproducts. The substitution of Equation (11) into Equation (7) results in an equation that mathematically describes the physicochemical process within the sensor:
The latter equation provides a mathematical description of how the concentration of ethanol changes, or in other words, how electrons are produced and how the electrical current evolves in a complex porous medium. However, the values of the parameters indicated by
(related to the change in diffusivity with time and position) are unknown and obtaining them is beyond the scope of this work. It is also important to mention that the change in ethanol concentration is not the only chemical reaction occurring on the sensor; further research is needed to derive an appropriate expression for the second exponential term. Therefore, it can be said that the exponential change in concentration is influenced by the time needed for the ethanol to fill the testing chamber. Ideally, the testing chamber can be saturated within nine seconds after the ethanol flows in. Consequently, it can be concluded that the exponential concentration term is related to the sensor filling time. Then, the logarithmic diffusion in Equation (12) may explain the complex behavior exhibited by the sensor, which is very similar to the Gompertz equation below:
where A is an asymptote value, B represents a positive displacement along the x-axis, and C sets the growth rate. The sigmoid function describes a growth pattern characterized by initial exponential growth, a middle period showing a gradual change, and a final stage of a designated mature phase. This parameterization suggests a future asymptote on the right side with a more gradual progression compared to its approaches towards the lower value asymptote from its beginning [
86]. Despite the complexity, this adapted mathematical model, derived from biological growth models [
87,
88], can elucidate the chemical and physical phenomena underlying the behaviors observed in the graphs generated by these SnO
2 and SnO
2-Fe sensors, as discussed earlier.
The proposed mathematical model consists of four stages, whichh provide a framework suitable for sensors manufactured using the proposed methodology Equations (14)–(17). These stages are the start (
), rise (
), sample (
), and decay (
) periods, each described by specific equations that outline their contributions to the overall model:
The fitting was conducted with the objective of comparing the SnO2 sensor’s performance against the SnO2-Fe sensor and other commercial MOX sensors. For the model, a plateau was established instead of an ascending curve. This plateau, set at 90% of the maximum value, has been reported by other types of sensors as its top signal limit. As predicted, an exponential relationship explains the adsorption, chemical reaction, and desorption phenomena on the sensor’s surface. It is assumed that commercial MOX sensors were originally designed to produce a similar ascending curve; however, this feature was subsequently removed through the implementation of electronic filters within the components of the common commercial MOX sensor.
After applying the proposed model to the SnO
2 sensor data, the model fits well at all measured temperatures and adequately represents the behavior of adsorption and desorption.
Figure 9a shows the sensor’s raw data at different temperatures, demonstrating good performance in the fitting across the temperature variations. In
Figure 9b, a commercial MOX sensor is also fitted using the same model function with the constants’ value presented above, indicating that this model can be used as a reference for future comparisons with other sensors in the literature.
Table 6 shows that for adsorption, parameters A and B increase with concentration, while parameter C remains constant. The slower desorption process is represented by the lower values of B and C compared to the adsorption values, which might be due to the higher polarity of the substances produced during the decomposition of ethanol (acetaldehyde, carbon dioxide, and water).
The mathematical model was also tested using different temperatures (
Table 7), provided that it can be correctly applied to the SnO
2 sensor. If the model accurately describes the behavior of the SnO
2 sensor across different temperatures and concentrations, it suggests two key points.
Firstly, the sensor’s response to ethanol follows a consistent pattern that can be effectively characterized by the Gompertz function, regardless of variations in the temperature of ethanol concentration. This consistency in sensor behavior across different environmental conditions indicates robustness and reliability in the sensor’s response. Secondly, the successful application of the model across various temperatures and concentrations underscores the versatility and adaptability of the sensor in diverse operating environments. It suggests that the sensor’s response dynamics are not overly influenced by external factors such as temperature variations or changes in ethanol concentrations, allowing for reliable and accurate measurements under different conditions.
The root mean square error (RMSE), lower than 7, indicates that the model fits well, not only to the SnO2 sensor’s experimental data at different temperatures but also to that of the commercial MOX sensor. In the context of the Gompertz model, RMSE represents the average magnitude of error between the actual response data and the response values predicted by the model.
The application of the model to the SnO
2-Fe sensor at various temperatures (
Figure 10) and concentrations (
Figure 10b–d) provides valuable insights into its sensing capabilities. By analyzing the sensor’s response using this mathematical framework, the dynamic behavior of the sensor concerning different environmental conditions can be elucidated. The Gompertz model, with its sigmoidal shape, aptly captures the non-linear relationship between the sensor output and the concentration of target gases across a range of temperatures. Through this analysis, critical points such as the detection threshold, saturation levels, and the rate of response can be discerned, offering a comprehensive understanding of the sensor’s performance under diverse operating conditions.
The application of the Gompertz model to the SnO
2-Fe sensor is demonstrated by its strong fit to experimental data, highlighting its effectiveness in capturing the complex relationship between sensor response and gas concentrations (
Table 8) at different temperatures (
Table 9). Furthermore, with root mean square error (RMSE) values around 30, the model’s predictive accuracy is noteworthy, indicating minimal deviation between predicted and observed values. This precision is essential for ensuring reliable and consistent sensor performance, reinforcing confidence in its capability to accurately detect and quantify target gases.
The consistency and robust fit of the model to the SnO2, SnO2-Fe, and commercial MOX sensors suggest a fundamental similarity in their sensing mechanism and response dynamics. This consistency highlights the model’s applicability in proving a comprehensive and reliable characterization of sensor behavior.
Ultimately, the successful application of the model to different sensors demonstrates its effectiveness in capturing the essential dynamics of gas sensing. The model not only offers a detailed understanding of the adsorption and desorption processes but also provides a reliable framework for comparing the performance of various sensors. This approach fosters further advancements in sensor technology, ensuring that future sensors can be accurately modeled, and their performance optimized for diverse applications.
In our study, we applied an exponential model to fit the dynamic response curves of Fe-doped SnO2 thin-film sensors. This approach allowed us to investigate the influence of Fe doping on sensor performance, specifically analyzing parameters A, B, and C. Parameter A represents the initial response magnitude, reflecting the baseline resistance change upon ethanol exposure. Parameter B is the rate constant for the exponential growth phase, indicating the response speed of the sensor. Parameter C is the rate constant for the exponential decay phase, representing the sensor’s recovery speed after ethanol exposure is removed. These parameters are crucial for understanding the sensor’s behavior, as Fe doping alters the electronic properties and surface chemistry of SnO2, enhancing adsorption sites and influencing interaction dynamics with ethanol molecules.
Our findings indicate that Fe-doped SnO2 sensors exhibit increased sensitivity and faster response times due to the catalytic and magnetic properties of Fe. This enhances the adsorption and desorption rates of ethanol, impacting parameters A, B, and C. Specifically, Fe doping can lead to higher values of A due to increased adsorption sites and higher values of B and C due to improved response and recovery speeds, respectively. These effects are particularly significant for polar gas molecules like ethanol, as the altered electronic properties of Fe-doped SnO2 enhance the interaction with polar molecules.
In contrast to other studies [
89], which focused on thick-film sensors with metal sandwich or co-planar electrodes and presented only a single plot of fractional conductance change, our work extends the application of the exponential model to thin-film sensors. Additionally, we provide a comprehensive analysis of the gas resistance signals and a detailed interpretation of the model parameters. This distinction highlights the novelty of our approach and its relevance in advancing the understanding of Fe-doped SnO
2 sensors for ethanol detection.