Electrical characterization of Ag/MoO_3−x/p-Si Schottky diodes based on MoO_3−x synthesized via sol–gel method: an investigation on frequency and voltage dependence

Transition metal oxides are extensively employed in various applications such as perovskite solar cells (PSCs), organic solar cells (OPVs), dye-sensitized solar cells (DSSCs), and light-emitting diodes (OLEDs) due to their high transparency in the visible spectrum, excellent conductivity, semiconductor properties, and elevated values of charge carrier mobility [1]. The initial studies on using transition metal oxides as anode buffer layers emerged in OLED device design [2]. Subsequent research on organic solar cell applications focused on efficient hole carrier transportation and extracting charge carriers from the solar cell to the electrodes [3, 4]. Commonly, titanium dioxide (TiO₂) and zinc oxide (ZnO) serve as cathode buffer layers, while anode buffer layers often feature metal oxide thin films such as nickel oxide (NiO) and vanadium oxide (V₂O₅), molybdenum trioxide (MoO₃). The primary reason for using metal oxides is to prevent the penetration of moisture and oxygen molecules present in the atmosphere into the active absorber layer of the solar cell and to enable constructive interference between the visible light incident on the active layer and the light reflected from the cathode electrode [5, 6]. Transition metal oxides such as MoO₃, tungsten oxide (WO₃), and V₂O₅ are widely used as anode ohmic contacts in both organic solar cells and OLED devices. These metal oxides have work functions exceeding 6 eV, forming a strong acceptor with organic materials [1].

Metal semiconductor (MS) contacts are one of the most important parts of organic based and inorganic based semiconductor devices. The interfacial states of metal semiconductor contacts dominate device reliability, stability, and performance due to the surface conditions of interlayer in MS contacts [7, 8]. The mechanisms governing current transport in these semiconductor devices depend on a variety of factors, including semiconductor fabrication parameters, the formation of insulating layers, temperature, and the applied bias voltage. Various theoretical models, including recombination generation, thermionic emission (TE), thermionic field emission (TFE), space charge limited current (SCLC) mechanisms, multi-step tunneling competition, and Poole–Frenkel, have been employed to clarify the complexities of charge transport phenomena [9‐12]. However, in certain special cases, two or more mechanisms may coexist. Nevertheless, a complete explanation of the transmission mechanisms through Schottky contacts remains a challenging problem. In most organic based devices, surface conditions of MS contact have been studied rarely compared to active semiconductor layer.

MoO₃, as a wide-bandgap semiconductor, exhibits various interesting properties such as relatively high chemical stability, high refractive index, and electronic properties, making it a promising material for numerous fundamental and applied fields [13]. These advantages of MoO₃ are crucial, making it an ideal candidate for various potential applications, such as transparent conductive coatings and buffer layers. MoO₃ thin films are predominantly manufactured through a range of physical and chemical deposition techniques, including sputtering, molecular beam epitaxy, and laser ablation. Additionally, chemical methods such as thermal evaporation, pulsed laser ablation and electro-deposition chemical vapor deposition (CVD) are employed in the production process [13‐15]. Although numerous studies have demonstrated the deposition of cathode layers (such as TiO₂ and ZnO) and anode buffer layers (such as MoO₃, V₂O₅, and NiO) using thermal evaporation method, it has recently been shown that these materials can also be obtained in solution form [7, 16, 17].

The sol–gel process is a versatile wet-chemical technique widely used to synthesize transition metal oxide semiconductors, which involves the transition of a liquid “sol” phase to a solid “gel” phase through hydrolysis and condensation reactions of molecular precursors. In the first step of this technique, homogenous solutions of high purity alkoxide precursor materials are obtained. Upon hydrolysis and condensation reactions, a gel is formed, which occupies the entire solution volume and forms a network [17]. The sol–gel approach allows significant control over composition and ensures high homogeneity, making it advantageous over other coating methods for all device applications where low process costs are a priority.

MoO₃ thin films can be deposited using a range of deposition techniques, including thermal evaporation, solvothermal processes, atomic layer deposition (ALD), and jet nebulizer spray pyrolysis (JNSP). Yu et al. reported an ideal factor of 1.77 for diodes fabricated using MoO₃ nanoplatelets deposited via thermal evaporation. However, when MoO₃ was coated with Ta₂O₅ and La₂O₅ materials using RF sputtering, their ideal factors increased to 5.92 and 5.23, respectively, exhibiting non-ideal diode behavior [18]. In 2015, Balaji et al. obtained a high ideality factor of 7.19 from the p-Si/MoO₃/Ag device. This device was produced by applying thin MoO₃ films onto the substrate at a temperature of 500 °C using JNSP, which resulted in films with the lowest activation energy and the largest crystallite sizes [19]. In 2016, Chen et al. achieved an ideality factor of 2.5 at 310 K from the Al/MoO₃/p-InP diode produced with MoO₃ thin film coated using thermal evaporation method [20]. Mahato et al. (2019) fabricated Au/MoO_3−x/n-Si devices using thermally evaporated MoO_3−x layer, which contained defects due to oxidation states. Remarkably, the devices achieved an ideality factor of 1.55 [21]. Vivek et al. investigated the impact of barium (Ba) doping on Cu/MoO₃/p-Si devices fabricated using JNSP. The addition of 15 wt% Ba²⁺ ions to MoO₃ thin films deposited at 500 °C resulted in significant improvements: positive photosensitivity, low saturation current, and large grain sizes. Furthermore, this doping strategy achieved an ideality factor of 1.92 [22]. In 2021, Çaldıran et al. coated MoO₃ layers on n-type and p-type silicon via thermal evaporation, obtaining ideal factors of 1.25 and 1.22 respectively, demonstrating that MoO₃ layer was more consistent on p-type silicon [23]. Özden reported an ideality factor of 1.54 for Al/MoO₃/p-Si devices with thermally deposited MoO₃ [24]. In 2021, the ideality factor of the Au/MoO₃/p-Si device, prepared by depositing a MoO₃ layer onto p-Si using the solvothermal method via thermal evaporation, was measured as 3.48 [25]. In 2022, Vivek et al. successfully improved the performance of Cu/Y-MoO₃/p-Si devices fabricated with JNSP. This improvement was achieved by incorporating yttrium (Y) into the MoO₃ layer, leading to a significant decrease in the ideality factor (from 5.4 to 1.7) [26]. In 2023, Basyooni et al. calculated a high ideality factor of 13.3 from the n-Si/MoO₃/Ag diode structure produced with MoO₃ deposited by ALD [27]. While MoO₃ thin films produced by these methods have been utilized in Schottky diode applications, there is a lack of studies focusing on MoO₃-based diode applications fabricated using the sol–gel method via spin coating, which is a facile technique, and discussing the sol–gel based MoO₃ oxidation steps.

Fully stoichiometric MoO₃ films exclusively contain Mo⁺⁶ cations, while an oxygen deficiency leads to the emergence of Mo⁺⁵ cations, followed by Mo⁺⁴ oxidation states, resulting in a partially filled Mo 4d-band within the band gap of MoO₃ [28]. Thermal evaporation of MoO₃ thin films can induce a deviation from stoichiometry, leading to the formation of non-stoichiometric MoO_3−x structures. This reduction process facilitates the transition of Mo cations from the + 6 oxidation state (Mo⁺⁶) to lower oxidation states (Mo⁺⁵, Mo⁺⁴, Mo⁺³). The resulting oxygen vacancies introduce defect states within the bandgap of MoO₃ [21]. This phenomenon is evident from the stark contrast in conductivity between MoO₃ (intrinsic semiconductor with low conductivity ~ 10^–7 S cm⁻¹) and MoO₂ (~ 10⁴ S cm⁻¹) [21]. The progressive decrease in the Mo cation oxidation state directly correlates with the observed improvement in electrical conductivity. Consequently, nonstoichiometric MoO_3−x thin films display favorable electrical conductivity, making them suitable for various optoelectronic device applications [29].

In this study, a comparative study was conducted to reveal effect of MoO_3−x interlayer used at the Ag/p-Si interface at room temperature. MoO₃ have been deposited by thermal method in reported studies widely [23, 30, 31]. MoO_3−x was synthesized by sol–gel technique in this study and deposited by spin coating technique. As far as we know, the use of sol–gel synthesized MoO_3−x structure in Schottky diode applications has not been reported. Therefore, this study has focused on the impact of Mo oxidation steps taking place across the bulk and at metal/metal oxide interfaces within MoO_3−x thin films fabricated through the sol–gel method and coated via spin coating technique on charge transport. X-ray diffraction (XRD) and X–ray photoelectron spectroscopy (XPS) techniques were employed for the structural characterization of MoO_3−x. Simultaneously, the electrical properties of Schottky diodes were assessed through room temperature I–V and C–V measurements. I–V, C–V, G–V, and F–V characteristics were systematically examined, and Schottky diode parameters, including n, \(\varnothing\)_bo, R_s, and N_ss, were determined for the Ag/MoO_3−x/p-Si Schottky diode.

The XRD pattern obtained from the MoO_3−x thin film annealed at 450 °C is illustrated in Fig. 1a. Sol–gel synthesized and annealed thin films exhibit well-defined orthorhombic α-MoO₃ structures, as evidenced by strong and sharp XRD peaks. The narrow full-width at half-maximum (FWHM) of these peaks aligns well with reported values for highly crystalline α-MoO₃ in literature, such as 2\(\theta\) = 12.8°, 23.5°, 25.7°, 27.4°, 33.6°, 39° and 49.4° corresponding to (020), (110), (040), (021), (111), (060), and (002) planes for orthorhombic α-MoO₃. The identified patterns match well with the standard data card number CPDS-05-0508 of the α-MoO₃ crystal symmetry [34]. XRD analysis reveals a strong preferential orientation for MoO₃ thin films. This is manifested in the XRD pattern by the intense peaks corresponding to the (020), (040), and (060) planes at 2θ angles of 12.84°, 25.74°, and 38.98°, respectively [34, 35]. The X-ray diffraction patterns presented in Fig. 1a enable us to calculate the interplanar spacing (d-hkl) for various crystallographic planes in α-MoO₃, identified by their Miller indices (h, k, l). By applying Bragg’s Law and utilizing these d-spacings, we can determine the unit cell parameters (a, b, and c) of the α-MoO₃ crystal lattice. The calculated values of unit cell parameters for the preferred orientation in the orthorhombic phase are a = 3.94 Å, b = 13.86 Å, and c = 3.69 Å which are in good agreement with previously reported data [34]. To assess the band gap of the MoO_3−x film, the absorption spectra were collected within the wavelength range of 300–900 nm. Through the application of the Tauc theory to analyze the absorption spectrum, a plot of (αhν)² − hν was generated, where α: is the absorption coefficient and hν: is the photon energy. The point where the linear region intersects the energy axis yields an approximate value for the band gap energy of MoO_3−x, determined to be 3.4 eV as illustrated in Fig. 1b [36].

To understand the oxidation state of the oxygen atom bonded with the molybdenum transition metal, XPS spectra were obtained in the binding energy range of 200–250 eV, which corresponds to the Mo 3d orbitals. Observed in Fig. 2a, the binding energies associated with the peak signals of the Mo 3d_5/2 and Mo 3d_3/2 orbitals are determined to be 233.7 eV and 236.8 eV, respectively. These determined values are consistent with the literature references, with reported values of 233.4 eV for Mo 3d_5/2 and 236.5 eV for Mo 3d_3/2. According to the XPS spectra, the reduction of Mo⁺⁶ cations in MoO₃ to Mo⁺⁵ occurs due to reactive interfaces. Similarly, the 3d_5/2 and 3d_3/2 levels exhibit binding energies of 232.4 eV and 235.5 eV, respectively, signifying the oxidation state of Mo⁺⁵. The results indicate that the Mo metal in the thin film obtained after synthesis is in the Mo⁺⁶ and Mo⁺⁵ oxidation states at surface [37‐39]. According to XPS depth profiling analysis, for the MoO_3−x thin film, while on the surface, it exhibits Mo⁺⁶ and Mo⁺⁵ oxidation states, as we move deeper into the bulk, the Mo⁺⁴ state is observed (Fig. 2b and Figure S1). The oxidation state of Mo⁺⁴ level corresponds to binding energies of 230 eV [38]. In the O 1 s high resolution spectrum of the MoO_3−x film, the first component, located at a lower binding energy (531.6 eV), is attributed to the lattice oxygen atoms involved in the MoO₃ bond within the oxide structure. The second peak observed in the O 1s spectrum, positioned at a higher binding energy (532.5 eV), is indicative of oxide impurities. Specifically, it corresponds to oxygen associated with defect or vacancy sites on the surface of the film. The oxygen defect content gradually increases in the bulk of the MoO₃ film (Figs. S2 and S3) [38]. This observation suggests the diversity present in the surface layers, particularly because of the range of oxidation states found within the XPS depth profile.

Surface characteristics of the MoO_3−x thin films were examined through AFM and SEM analyses, with Fig. 3a depicting the AFM image obtained at an annealing temperature of 450 °C and revealing a root mean square (RMS) value for the MoO_3−x film measuring 11.2 nm. The SEM image shows clear grains and boundaries, and homogeneous film surface is obtained (Fig. 3b) [40‐42]. The film surface of MoO₃ synthesized by the sol–gel method has a morphology with flower-like anisotropic structures. While crystallite sizes vary between approximately 10–21 nm, the size of each flower-like structure is quite different from each other, but they form a homogeneous surface.

In accordance with the thermionic emission (TE) theory, only charge carriers with energy higher than the potential barrier can generate diode current by passing over the barrier. In the transfer of charge from semiconductor to metal, charge carriers are required to navigate through the depletion region via drift and diffusion currents, facilitated by the presence of an electric field. Once the charge carriers reach the interface, their emission into the metal is dictated by the transfer rates across the interface. These two mechanisms are in series, and the dominant mechanism for current conduction is the one that offers the maximum resistance to charge carrier transfer. The net current–voltage relationship in Schottky diodes is described by Eq. 1 [43‐46].

Here, I₀: saturation current, q: the electron charge, n: the ideality factor, k: the Boltzmann constant, T: the temperature in Kelvin and V: the applied voltage. The expression for the I₀ is articulated as:

A = the rectifier contact area (7.85 × 10^–3 cm²), A* = the Richardson constant (32 A/cm²K² for p-Si) [46‐48], and \(\varnothing\)_b0: zero-bias barrier height.

In accordance with the thermionic emission model, the determination of the n value involves extracting it from the slope of the lnI–V, while the value of \(\varnothing\)_b0 at zero bias condition can be obtained from the intersection of the graph. Figure 4 displays the I–V plots of the Schottky diodes, depicted on a logarithmic scale. The Ag/p-Si diode exhibited a rectification ratio of 6.5 × 10³, determined by the ratio of maximum to minimum currents at a fixed voltage (V =  ± 2 V). In contrast, the Ag/MoO_3−x/p-Si diode exhibited a significantly higher rectification ratio under the same conditions, measured at 2.9 × 10⁵. The parameter n characterizes the deviations from ideal diode behavior and is as an indicator of device quality. To perform the calculation, it is necessary to examine the slopes of the linear segments within the natural logarithm of the lnI–V characteristics under forward bias conditions, employing the expression V > 3 kT q⁻¹.

At room temperature, the ideality factors were calculated as 2.4 for Ag/p-Si and 1.9 for Ag/MoO_3−x/p-Si. The calculation of the barrier height (\(\varnothing\)_b0) is achieved by employing the reverse saturation current (I₀), as defined in Eq. 2. This results in values of 2.4.10^–5 and 6.4.10^–9 for Ag/p-Si and Ag/MoO_3−x/p-Si, respectively, obtained through the intercept of the lnI under zero bias conditions. The determination of the \(\varnothing\)_b0 at zero bias can be achieved using Eq. 3. For the Ag/p-Si reference and Ag/MoO_3−x/p-Si diode configurations, the determination of the \(\varnothing\)_b0 is derived from the I–V graph, resulting in values of 0.54 eV and 0.69 eV, respectively.

The logarithmic current–voltage (lnI–V) graph in Fig. 5a typically exhibits a linear behavior in the low-voltage regions of the forward bias current. Deviations in the linear region become apparent as the voltage value increases. These deviations can be ascribed to the resistance introduced by the interface material and the utilization of interface states between the metal and the semiconductor [49, 50]. In the Schottky diode electrical properties, the R_s stands out as a critical parameter for analysis [51]. The Cheung–Cheung method is employed as one of the techniques for assessing the R_s. Within the Cheung–Cheung method, the parameters R_s, n, and \(\varnothing\)_b0 can be determined.

Applying Eq. 6 to the dataset associated with the region of downward curvature in the forward bias I–V graph is anticipated to result in a linear relationship. Consequently, through the plotting of dV/d(lnI)–I graph, the R_s can be ascertained from the slope, measuring as 1.3 kΩ and 1.8 kΩ for Ag/p-Si and Ag/MoO_3−x/p-Si, respectively. The evaluation of H(I) using Eq. 8 and its subsequent plotting against I, presented in Fig. 5b, also yields a linear pattern. In this pattern, the y–axis intercept corresponds to \(\varnothing\)_B, while the slope represents R_s, providing validation for the methodology advocated by Cheung–Cheung. The calculated parameters for the device include a \(\varnothing\)_b0 of 0.56 eV and a R_s of 1.9 kΩ for Ag/p-Si, while for Ag/MoO_3-x/p-Si, the values are 0.83 eV and 7.1 kΩ, respectively.

The Norde method, another technique devised for determining R_s, serves as an appropriate approach for calculating the barrier height of the diode [52]. The Norde method relies on analyzing the H(I)–I graph, where the R_s is derived from the slope, and the value of \(\varnothing\)_B is obtained from the intersection of the graph. The determination of \(\varnothing\)_B is accomplished by identifying the intersection point on the graph.

The Norde method has the advantage of being a suitable technique for calculating the barrier height, but its disadvantage lies in the difficulty of accurately identifying the minimum point on the graph The Eq. 9 representing the Norde method is as follows.

Here, I signifies the current extracted from the experimental I–V values, while γ represents a dimensionless arbitrary integer surpassing the n deduced from the lnI–V graph. γ is set to 2 and 3 for Ag/MoO_3−x/p-Si and Ag/p-Si, respectively. Plotting F(V) against V allows for the calculation of the diode’s \(\varnothing\)_B at the point of minimum F(V₀), corresponding to the lowest voltage V₀ along the F(V)–V curve (Fig. 6). The barrier height is expressed as follows:

The expression for the R_s is as follows,

The \(\varnothing\)_B and R_s are calculated using Norde’s method, resulting in values of 0.58 eV and 3.2 kΩ for Ag/p-Si, and 0.78 eV and 33.8 kΩ for Ag/MoO_3−x/p-Si, respectively. The Norde method operates under the assumption of an ideal contact between metal/semiconductor (i.e., n = 1), leading to variations between the I–V and the Norde method. Data extracted from the linear region of the curve, emphasizing the effects of N_ss and interfacial layers, is employed by both the I–V and the Norde method. In the Cheung–Cheung method, the determination of \(\varnothing\)_B values relies on data extracted from the nonlinear-region of the I–V graph. This region not only accounts for R_s but also considers the impact of interfacial layers and N_ss. Due to the utilization of distinct regions in the lnI–V by each method, discrepancies emerge in the barrier height values. Table 1 presents the frequency dependence of R_s values obtained through various methods. The R_s values calculated using all methods exhibit variations from one another. Cheung–Cheung functions are specifically utilized in the lnI–V characteristic characterized by downward curvature. Nonetheless, Norde functions are employed across the entirety of the forward bias region in the lnI–V. Consequently, R_s values extracted from Norde plots exhibit a considerable increase compared to those determined through Cheung–Cheung functions and the I–V method. Additionally, the inconsistency may be attributed to the challenge of precisely determining the minimum points on F(V)–V plots. Within the Norde method, the R_s value is extracted from the linear region of the lnI–V characteristic, where the current exhibits exponential variations. Thus, even a small error in identifying graphical turning points may have a notable impact on accurately determining the R_s value [51‐53].

Apart from the current conduction mechanism, the thickness of the interface layer has an impact on the electrical parameters of semiconductors in Schottky diodes. Moreover, the density of N_ss plays a critical role by effecting the performance and quality of electronic devices [50, 54]. The concentration of N_ss significantly affects both n and \(\varnothing\)_B values. As the interface layer between the semiconductor and metal thickens, the probability of current conduction diminishes. The voltage dependent N_ss is expressed as follows:

The measured thickness of the MoO_3−x thin film, recorded using a profilometer, is 46 nm. Here, \({\varepsilon }_{i}\): permittivity of the insulator layer, \({\varepsilon }_{s}\): the permittivity of the semiconductor, W_d: the width of the space charge region and d: the thickness of the insulator layer. The expression for the W_d is given by [44],where \({\varepsilon }_{s}\)=11.8 \({\varepsilon }_{0}\), V₀ stands for the built-in potential determined by extrapolating the 1/C²–V curve on the voltage axis. The semiconductor acceptor density (N_A) is determined as 1 × 10¹⁷ cm⁻³ from the slope of the 1/C²–V. This curve, derived from the depletion capacitance based on Eq. 14 at 1 MHz, is illustrated in Fig. 7 [23]. The resulting calculated value for W_D is 149 nm.

The voltage–dependent effective \({\varnothing }_{e}\) is expressed as follows:

Here, β: voltage coefficient of the effective \({\varnothing }_{e}\). For p-type semiconductors, the expression for the energy of E_ss in relation to the top of the valence band at the semiconductor surface is expressed as:

In Fig. 8, the N_ss demonstrated variability within the range of 2.1 × 10¹² to 2.5 × 10¹² eV⁻¹ cm⁻². Owing to reactive interfaces, the Mo⁺⁶ cations within MoO_3−x undergo reduction to Mo⁺⁵ and Mo⁺⁴, which is evident from the XPS spectra showing interfacial reduction. This reduction causes a deficiency of oxygen, resulting in the formation of defect states within the MoO_3−x. The reduction in oxidation results in the generation of defects between the valence and conduction bands, which play a significant role in facilitating charge transport. As a result, electrons have the capability to move from the silicon (valence band) to the MoO_3−x (conduction band) due to the existence of these defect states [38]. Hence, the presence of defects influences the current conduction within the MoO_3−x film [38, 55]. In examining the interface properties of the Ag/MoO_3−x/p-Si, we conducted capacitance–voltage (C–V–f) analyses across a frequency spectrum ranging from 10 kHz to 1 MHz, as depicted in Fig. 9 [56]. As the frequency decreases within the range of 10 to 1000 kHz, the capacitance of the diode exhibits an increase. The rise in capacitance at lower frequencies is due to the existence of N_ss. At these frequencies, the N_ss align with the alternating current signal, resulting in the direct parallel inclusion of capacitance from N_ss along with the depletion capacitance. Consequently, this leads to an increased overall capacitance. With an increase in frequency, the N_ss are unable to track the alternating current signal, and instead, they assume constant values. The interface state charges that have no impact on the diode capacitance result in lower capacitance values. Consequently, as the frequency was progressively raised, the capacitance of the Schottky diode initially decreased and eventually stabilized at an almost constant level.

The capacitance–voltage (C–V) analyses across a frequency spectrum ranging from 10 kHz to 1 MHz with a fixed alternating (AC) signal (10 mV) were carried out in order to examine the interface properties of the Ag/MoO_3−x/p-Si [56]. C–V and G–V measurements reveal a significant dependence of both device capacitance and conductance on applied voltage and measurement frequency. These dependencies manifest as distinct regions in the C–V and G–V curves, corresponding to the inversion, depletion, and accumulation regimes. These regions are observed with negative, moderate, and high bias voltages, respectively, as illustrated in the Fig. 9. Within the inversion region, capacitance values typically remain unaffected by variations in voltage (V). However, as V progresses towards the accumulation region, both parameters start to increase. C–V curves at lower frequencies exhibit a peak due to N_ss, contingent upon their relaxation time (τ). At higher frequencies, a peak emerges in the C–V curve within the accumulation region. This peak is primarily caused by the series resistance present in the device [57].

Figure 10 illustrates the G–V behavior of the Ag/MoO_3−x/p-Si, demonstrating its sensitivity to both bias voltage and frequency at room temperature. The conductance characteristics are influenced by the presence of electronic states within the energy band gap, which are a consequence of factors such as dangling bonds, periodic disorder or surface states occurring at the interface. The characteristics of both C–V and G–V in the device are significantly influenced by these electronic states [58, 59].

Equation 17 is utilized to calculate the R_s of the Ag/MoO_3−x/p-Si device by incorporating the capacitance and conductivity with the diode equivalent circuit. Both the frequency and applied bias voltage exert a notable influence on the behavior of R_s. Additionally, the plots depicting R_s–V reveal a distinct peak near − 0.16 V, and this peak’s intensity fluctuates with frequency owing to the specific distribution of surface states. Moreover, the magnitude of this peak diminishes as the frequency increases, as illustrated in Fig. 11 [55, 60]. The occurrence of this peak is tied to the specific distribution of surface states, and as the frequencies increase, its magnitude experiences a reduction. Furthermore, the peak’s intensity increases at lower frequencies, accompanied by a shift in its position towards the negative bias region. This shift is a result of the rearrangement and restructuring induced by the applied voltage across various frequencies [60].

In this study, MoO_3−x was synthesized through the sol–gel method. Subsequently, the solution was applied on p-Si using the spin-coating technique, followed by the extraction of parameters for the Schottky diode. Following coating through the sol–gel method, the oxidation steps on the surface and within the bulk were revealed through XPS depth measurements after annealing at 450 °C. These distinct oxidation steps such as Mo⁺⁶, Mo⁺⁵ and Mo⁺⁴ led to heterogeneous barrier heights at the interface, thereby impacting diode performance. AFM and SEM images provided visual evidence of the development of a remarkably uniform MoO_3−x thin film. The Ag/MoO_3−x/p-Si device’s I–V, C–V, G–V and F–V analysis was assessed over a frequency range of 10 kHz to 1 MHz and a voltage range of − 2 V to + 2 V at room temperature. Under dark condition, the Cheung–Cheung and Norde methods were employed to calculate the basic device parameters ∅_B, n, and R_s. At room temperature, the exploration of MoO_3−x’s effects on N_ss, particularly Mo⁺⁶ and Mo⁺⁵, along with R_s, has been conducted by employing C–V–f and G–V–f techniques. The densities of N_ss and R_s are significantly impacted by both applied frequency and voltage. Additionally, the distribution of N_ss within the interfacial layer plays a substantial role in influencing N_ss, R_s, and n. The R_s–V plots, obtained through analysis of C and G data at various frequencies, reveal a consistent trend: the magnitude of the peak diminishes with increasing frequency. The characteristic behavior of this peak is associated to the existence of N_ss, coupled with the effects of R_s. The I–V characteristics were utilized to derive the energy density distribution profile of N_ss across a spectrum of forward bias voltages, extending from 2.1 × 10¹² to 2.5 × 10¹² eV⁻¹ cm⁻². Consequently, the observed low values of N_ss affirm the suitability of the fabricated Ag/MoO_3−x/p-Si with sol–gel based MoO_3−x Schottky diode for use in electronic device manufacturing within the electronics industry.