*3.3. Humidity-Sensing Mechanism*

The complex impedance curve is an effective method to study the properties of humidity sensing [26]. In AC complex impedance analysis, an AC sinusoidal test signal is applied to a thin-film device, and the frequency of the test signal is changed within a certain range. Figure 7 shows the complex impedance spectrum of the BiFeO<sup>3</sup> film in the range of 30–90% RH and in the scanning frequency range of 10–1000 kHz. The complex impedance spectrum of the BiFeO<sup>3</sup> film presented a circular arc shape when the RH was lower than 50%, as shown in Figure 7a–c. The complex impedance spectrum gradually changed from a circular arc to a semicircular shape with increasing humidity. Compared to the complex impedance spectra of standard circuit components, it can be concluded that the equivalent circuit diagram for BiFeO<sup>3</sup> films in the low-humidity range is composed of parallel connections of resistors and capacitors, as shown in Figure 7h. Oxygen ions and metal ions are exposed on the surface of the BiFeO<sup>3</sup> film, and the H2O molecules on the surface dissociate into H<sup>+</sup> and OH−. Then, OH<sup>−</sup> and H<sup>+</sup> are chemically combined with metal ions and oxygen ions, respectively, to form hydroxyl groups that constitute the first layer of physical adsorption [23]. The charge transfer is carried out according to the Grotthuss chain reaction of 2 H2<sup>O</sup> <sup>→</sup> <sup>H</sup>3O<sup>+</sup> + OH−, which has a weak influence on the capacitance of the BiFeO<sup>3</sup> film. H3O<sup>+</sup> spontaneously transfers H<sup>+</sup> to the second water molecule according to H3O<sup>+</sup> <sup>→</sup> <sup>H</sup>2O + H<sup>+</sup> [27,28], and the main mechanism underlying the humidity response is based on proton transport [29].

When RH increased to 70%, the complex impedance spectrum of the BiFeO<sup>3</sup> film showed a straight line with a slope of approximately 1 at frequencies from 10 to 100 Hz, as shown in Figure 7d,e. On top of the first layer of physical adsorption, more adsorption layers are formed through hydrogen bonding to generate a liquid water layer, and the physical adsorption changes from single-layer to multi-layer [30]. When RH increased to 90%, the proportion of the straight-line part of the complex impedance spectrum increased, while the semicircle part was compressed. The appearance of a straight line in the low-frequency region of the complex impedance spectrum indicates that the BiFeO<sup>3</sup> film has a significant Warburg impedance due to ion diffusion, as shown in Figure 7f,g. The corresponding equivalent circuit includes resistance, capacitance and Warburg impedance, as shown in Figure 7i. With the continuous increase in the number of adsorbed water molecules, the adsorption on the sample surface evolves into multi-molecular layer adsorption. The surface of the BiFeO<sup>3</sup> films is covered by water, resulting in a rapid increase in the amount of H<sup>+</sup> , which further increases the conductivity [31,32].

The *I*–*V* characteristics of the BiFeO<sup>3</sup> film at different RH levels are presented in Figure 8. The inset is a partial enlarged view of the change in *I*–*V* with RH. At different RHs, BiFeO<sup>3</sup> film exhibited linear *I*–*V* characteristics, which indicates an ohmic contact between the BiFeO<sup>3</sup> film surface and electrodes. Since the resistance was constant over the range of supply voltage, the sensitivity was the same regardless of the operating bias, which allows operation at low power in practical application [33]. As RH increased, the conductivity of the BiFeO<sup>3</sup> film increased, resulting in a decrease in current. The excellent humidity response makes BiFeO<sup>3</sup> films a potential candidate for practical humiditysensing applications.

**Figure 7.** The complex impedance properties of BiFeO<sup>3</sup> film under different humidities. (**a**) 30% RH; (**b**) 40% RH; (**c**) 50% RH; (**d**) 60% RH; (**e**) 70% RH; (**f**) 80% RH; (**g**) 90% RH. (**h**) The equivalent circuit fit by Zview in the 30−50% RH range. (**i**) The equivalent circuit fit by Zview in the 60−90% RH range.

**Figure 8.** Dependence of current on voltage for the BiFeO3 film at various RHs. Inset: the enlarged *I*–*V* vs. %RH plot (30–40% RH range). **Figure 8.** Dependence of current on voltage for the BiFeO<sup>3</sup> film at various RHs. Inset: the enlarged *I*–*V* vs. %RH plot (30–40% RH range).

**Figure 7.** The complex impedance properties of BiFeO3 film under different humidities. (**a**) 30% RH; (**b**) 40% RH; (**c**) 50% RH; (**d**) 60% RH; (**e**) 70% RH; (**f**) 80% RH; (**g**) 90% RH. (**h**) The equivalent circuit fit by Zview in the 30−50% RH range. (**i**) The equivalent circuit fit by Zview in the 60−90% RH range.

The *I*–*V* characteristics of the BiFeO3 film at different RH levels are presented in Figure 8. The inset is a partial enlarged view of the change in *I*–*V* with RH. At different RHs, BiFeO3 film exhibited linear *I*–*V* characteristics, which indicates an ohmic contact between the BiFeO3 film surface and electrodes. Since the resistance was constant over the range of supply voltage, the sensitivity was the same regardless of the operating bias, which allows operation at low power in practical application [33]. As RH increased, the conductivity of the BiFeO3 film increased, resulting in a decrease in current. The excellent humidity response makes BiFeO3 films a potential candidate for practical humidity-sensing applica-

### **4. Conclusions 4. Conclusions**

tions.

The BiFeO3 film prepared in this study via a simple sol–gel method exhibited significant humidity sensitivity with capacitance and impedance changes of nearly 2–3 orders of magnitude as RH increased from 30% to 90%. In the whole humidity range, the experimental results of humidity hysteresis and humidity response recovery indicate that BiFeO3 film is an excellent material for application in humidity sensors. The BiFeO<sup>3</sup> film prepared in this study via a simple sol–gel method exhibited significant humidity sensitivity with capacitance and impedance changes of nearly 2–3 orders of magnitude as RH increased from 30% to 90%. In the whole humidity range, the experimental results of humidity hysteresis and humidity response recovery indicate that BiFeO<sup>3</sup> film is an excellent material for application in humidity sensors.

**Author Contributions:** B.L. conceived and designed the experiments; Y.Z. and Y.J. revised the paper and contributed materials/reagents. All authors have read and agreed to the published version of the manuscript. **Author Contributions:** B.L. conceived and designed the experiments; Y.Z. and Y.J. revised the paper and contributed materials/reagents. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the National Natural Science Foundation of China (Grant Numbers: 51872264, 22179108), Shaanxi Provincial Natural Science Foundation of China (Grant Number: 2020JM-579), Key Research and Development Projects of Shaanxi Province (Grant Number: 2020GXLH-Z-032). **Funding:** This work was supported by the National Natural Science Foundation of China (Grant Numbers: 51872264, 22179108), Shaanxi Provincial Natural Science Foundation of China (Grant Number: 2020JM-579), Key Research and Development Projects of Shaanxi Province (Grant Number: 2020GXLH-Z-032).

**Institutional Review Board Statement:** Not applicable. **Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable. **Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available on request from the corresponding author.

**Conflicts of Interest:** There are no conflict to declare.
