1 Introduction

Globally, accomplishing energy-efficient management in the commercialization of electronic devices for microelectronic and optoelectronic applications is challenging. Schottky barrier diodes (SBDs) such as metal-semiconductor (MS) and metal-insulator-semiconductor (MIS) diodes exhibit superior electrical properties when compared to other layered diodes such as P–N, Zener diodes, metal-insulator-metal (MIM), crystal diodes, tunnel diodes, and LEDs [1,2,3]. SBDs operated with a low forward bias level (0.2–0.3 V) can be employed in high frequency switching applications [4, 5]. MIS SBDs also play a vital role in various applications, including biological sensors, microelectronic devices, optical communication systems, and the generation of radio frequencies, owing to their excellent mechanical stability [6, 7]. An inorganic/organic insulating layer deposited in between a semiconductor substrate and a metal electrode would change the value of Schottky barrier height (SBH/Φb) at the formed junction [8]. Multiple methods have been employed to use a SiO2 insulating layer at the interface of the metal-semiconductor diodes. According to previous literature, the SiO2 insulating layer results in a significant leakage current. Therefore, alternative interfacial insulating layers to lower the leakage current of MIS diodes are essential [9]. High-k dielectric/two-dimensional (2D) materials such as TiO2, MoO3, SnO2, HfO2, ZrO2, Si3N4, and In2O3 and with conventional metal electrodes (Au, Cu, Pt, Ti, Al, Mo, Sb, and Ni) attract considerable attention as interfacial layers and metal electrodes [10, 11]. The leakage currents of metal/ZrO2, metal/HfO2, metal/TiO2, and metal/Si3N4 junctions on the semiconductor substrate have extremely low leakage currents compared to metal/SiO2/semiconductor diodes. Furthermore, the use of high-k oxide layers increases the rate of rectification (RR = IF/IR)/shunt resistance [12,13,14]. Many previous studies have shown that high-k materials with higher dielectric constants can considerably improve the leakage current and carrier mobility of 2D semiconductors by minimizing Coulomb impurity scattering [15, 16].

ZrO2 has been extensively investigated over the past decade owing to its suitable features, such as high thermal stability, high dielectric constant (20–25), wide bandgap (5.8–7.8 eV), ion-exchange capability [17], high ionic conductivity, low thermal conductivity, higher strength/melting point, and good chemical stability at the Zr/Si interface [18]. ZrO2 material crystallizes into three phases at different temperatures: cubic (> 2370 °C), tetragonal (1170–2370 °C), and monoclinic (< 1170 °C). These characteristics make ZrO2 an excellent material for use in solar cells [19], batteries [20], photocatalysis [21], fuel cells [22], gas sensors [23], heterojunctions [24], photonics [25], and electrochemical capacitors [26]. The improved device properties of high-electron-mobility transistors (HEMTs) utilizing in situ produced silicon nitride (Si3N4) have demonstrated prospects for use in a wide range of electronic devices [27,28,29]. Due to its outstanding dielectric strength (˃ 107 V/cm), diffusion barrier, and high dielectric constant (~ 7.5), Si3N4 has been extensively investigated over the last decade. Si3N4 is also a good passivating dielectric for semiconductors such as Si and GaN with reduced surface densities [30]. The stoichiometry of Si3N4 is influenced by the deposition conditions employed [31]. Furthermore, because the insulating layer thickness influences the device performance, a thin insulating layer is necessary for good switching behavior [32, 33]. Therefore, investigating the characteristics of ultrathin interlayers (single/few layers) is challenging [1, 5, 16, 23, 24, 34,35,36,37,38, 66]. To reduce the interfacial defects in 2D devices, high dielectric constant and broad-bandgap materials are essential [16].

Because of their high specific surface area, atomically thin layers, single layers, or two-dimensional (2D) materials are attractive as channel materials for electronic and optoelectronic device applications [16]. Further, investigating the interaction of 2D materials with semiconductor substrates at interfaces with functional oxides and multifunctional devices with novel properties via coupling is important. These findings can provide insights for innovative 2D device modulation via functional oxide interface engineering. The current study focuses on the development of Mo/Si3N4/n-Si and Mo/ZrO2/n-Si (metal-insulator-semiconductor; MIS) single layers and Mo/Si3N4/ZrO2/n-Si (metal-insulator-insulator-semiconductor; MIIS) double interlayer SDs. In addition, to increase the performance and stability of the devices, the researchers used high-work function metals to prepare Schottky devices. The work function values of Pt, Au, Cr, Ag, Mo, and W, are 5.65, 5.1, 4.5, 4.26, 4.6, and 4.55 eV, respectively. Molybdenum (Mo) metal is used as a Schottky metal in this work; Mo metal gave the ReRAM properties with good work function (4.6 eV) [39]. The metals Au and Pt are very expensive and have a much higher work function value. And which is a standard electrode material with excellent electrical properties. So, the rectangular Mo metal electrodes were deposited on an n-Si substrate, and MIS/MIIS was compared with the MS diode. The optical, microstructural, chemical, and surface morphological characteristics of Si3N4, ZrO2, and Si3N4/ZrO2 films were examined. Finally, current–voltage (I–V) characteristics at room temperature were used to examine the electrical characteristics of the Mo/Si3N4/ZrO2/n-Si (MIIS) SD. The results of Mo/Si3N4/n-Si, Mo/ZrO2/n-Si (MIS) SDs, and MS SDs could be correlated with the MIIS SDresults.

This study's major objective is to investigate into how the Mo/n-Si SD's electrical properties are affected by the (Si3N4/ZrO2) double interlayer.For this purpose, (Si3N4 and ZrO2) were fabricated by the sputtering method and both their electrical, optical, microstructural chemical properties were investigated by UV–Vis-NIR spectrophotometry, grazing index X-ray diffraction (GIXRD), field emission scanning electron microscopy (FESEM), energy-dispersive X-ray spectroscopy (EDX), X-ray photoelectron spectroscopy (XPS), and atomic force microscopy (AFM) were used to analyze the optical properties. Following that, their n, BH, and RS values were determined and compared using the TE emission, Cheung's, Norde's, and SP-V techniques. These findings demonstrate that compared to the individual Si3N4 and ZrO2 single interlayer and without interlayered Mo/n-Si SDs, the (Si3N4/ZrO2) double interlayer leads to an increase in BH and a decrease in n and RS resultant values.

2 Experimental and characterizations techniques

In this study, 1 cm × 1 cm Si sample pieces from an 8″ Si (100) wafer with a thickness of 600 μm was used. To develop n-Si-based SDs, Si3N4 and ZrO2 interlayers were used. The RAC technique was used on a regular clean n-Si wafer with a resistivity of 1–10 Ω cm prior to deposition [40]. A HF: H2O (1:8) solution was used to remove native oxides, followed by rinsing in deionized water. To obtain a satisfactory ohmic contact, thermal evaporation was used to generate an Al metallization of 45 nm thickness on the back (rough) side of the cleaned substrate (Si), which was annealed at 300 °C for 5 min in N2 gas using a rapid thermal processing furnace. Thereafter, RF-magnetron sputtering was used to deposit Si3N4 and ZrO2 thin films on the n-Si (smooth side) and quartz glass substrates. Si3N4/Si diodes (three samples) were prepared using a 50 mm diameter Si3N4 target (99.9% purity) in ambient air of argon as the sputter gas. ZrO2/Si (three samples), and Si3N4:ZrO2/Si (three samples) diodes were also prepared under the same deposition conditions. To remove surface contamination, the target was pre-sputtered for 10 min in an Ar gas environment. Finally, using direct current sputtering equipment, Mo was deposited as a top metal electrode with a thickness of 40 nm in a rectangular area of 1.2 mm × 0.3 mm under the conditions listed in Table 1. The Mo/Si3N4/Si, Mo/ZrO2/Si, and Mo/Si3N4/ZrO2/Si SDs are shown schematically in Fig. 1a, b, respectively. To compare the electrical characteristics, interlayered SDs (MIS) without interlayered SDs (MS) were developed under identical conditions. UV–Vis-NIR spectrophotometry, GIXRD, FESEM, EDX, XPS, and AFM were used to analyze the optical, microstructural, elemental, morphological properties, and chemical composition of the prepared Si3N4/Si, ZrO2/Si, and Si3N4/ZrO2/Si devices. Finally, the electrical characteristics of the Mo/n-Si (MS) SD and Mo/Si3N4/Si, Mo/ZrO2/Si (MIS), and Mo/Si3N4/ZrO2/Si (MIIS) (single/double interlayer) SDs were investigated at room temperature using a Keithley source meter (2636).

Table 1 Deposition parameters of Si3N4, ZrO2 thin films, and Molybdenum metal electrode
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Fig. 1
figure 1

Schematic configuration of the fabricated Mo/Si3N4/n-Si, Mo/ZrO2/n-Si (MIS), Mo/Si3N4/ZrO2/n-Si (MIIS) (single layer and double layer) SDs

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3 Results and discussion

3.1 Evaluation of optical, microstructural, surface morphology, chemical, and electrical properties

3.1.1 Optical absorption study

UV–Vis-NIR spectroscopy was used to analyze the electronic structures of the Si3N4, ZrO2, and Si3N4:ZrO2 films at ambient temperature. Absorption was caused by the electronic transitions inside the Si3N4 and ZrO2 materials. Figure 2 shows the UV–Vis spectra of the single layer and double interlayer coatings on quartz. The double interlayer film displayed a color shift from blue to violet compared to the single-layer films. The highest absorbance for the double interlayer film was obtained at approximately 266 nm, with a peak at 209 nm, as shown in Fig. 2c. Furthermore, beyond 280 nm, the absorbance remained constant up to 1000 nm. The double interlayer shifts the values of absorption to a greater wavelength range than the single layer because of the deep black pigmentation of the films, roughness of the surface, and increase in grain boundaries, in addition to the stimulation or transfer of charge carriers (Fig. 2a) [41, 42]. Tauc’s plot was used to determine the direct optical bandgap (Eg) in the single and double interlayer films, as shown in Fig. 2b, c. The resulting Tauc plot can be used to estimate the direct Eg by extrapolating the (αhν)2 vs. ‘hν’ curve below zero absorbance [43]

$$\alpha {\text{h}}\nu = {\text{E}}_{{\text{D}}} \left( {{\text{h}}\nu - {\text{E}}_{{\text{g}}} } \right)^{{{1}/{2}}} ,$$
(1)

where ED is a constant, hν is the photon energy, and α is the absorbance coefficient.

Fig. 2
figure 2

a Absorbance-wavelength spectrum, b Tauc’s plot: (αhν)2-hν for Mo/Si3N4/n-Si, Mo/ZrO2/n-Si(MIS) SDs, and c absorbance-wavelength spectrum and Tauc’s plot: (αhν)2-hν for Mo/Si3N4/ZrO2/n-Si (MIIS) SD

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The Eg values of bulk Si3N4 and ZrO2 were 5.3 and 4.9 eV, respectively. The single and double interlayer films had direct bandgap energies of 5.20, 4.31, and 3.90 eV, respectively. These results agree with those of previous studies [44, 45]. Because of the increased Fermi energy level, single-layered films have a larger bandgap than double-layered films. This could be due to the production of O2 vacancies in the Si3N4, and ZrO2 sites and crystalline formation, which minimized defects [46]. These findings affect the electrical transitions between the VB and CB (valence and conduction bands), which reduces the energy values of the Si3N4:ZrO2 film. An uncoated quartz substrate was used as the baseline correction reference for optical absorption.

3.1.2 X-ray diffraction study

The grazing incidence x-ray diffraction (GIXRD) scans of the Si3N4, ZrO2, and Si3N4:ZrO2 films on Si are shown in Fig. 3. Si3N4 showed a significant intensity reflection of the (3 2 0) and (1 0 4) planes of α-Si3N4 at 2θ values of 34.46° and 59.26°, respectively, indicating the existence of hexagonal instead of amorphous [36, 38] (Fig. 3a). The high-intensity refractions of ZrO2 (1 0 1), ZrO1.99 (0 0 2), ZrO2 (1 1 0), and ZrO2 (2 1 1) planes are shown in Fig. 3b at 2θ values of 30.55°, 33.37°, 35.30°, 50.56°, and 60.26° confirming the predominant tetragonal phase. Figure 3c, d show the as-deposited and annealed XRD plot of Si3N4:ZrO2 thin films on n-Si, respectively. Figure 3c shows the high-intensity refractions of the ZrSiO4 (2 0 0), Zr7O11N2 (0 0 6), Zr2ON2 (4 0 0), Zr7O11N2 (1 2 8), ZrSi2(1 7 1), ZrSiO4 (4 1 1), and Zr7O11N2 (2 1 10) planes at 2θ values of 27.11°, 30.51°, 35.36°, 50.76°, 56.18°, 59.43°, and 60.48°, respectively. We observed new phases owing to the combination of two layers, which proved the existence of tetragonal rather than rhombohedral or orthogonal phases. Figure 3d shows the Si3N4:ZrO2 thin film at 500 °C for 10 min in an N2 atmosphere to verify its crystallinity. Compared with the as-deposited films, the intensity of the annealed film increased. This indicates that the Si3N4:ZrO2 interface formed an interfacial phase after annealing. XRD results revealed that the single layer and double interlayer films deposited on n-Si had a significant impact on the electrical characteristics of both SDs [47, 48].

Fig. 3
figure 3

XRD spectrum for a Si3N4, b ZrO2, and c, d Si3N4/ZrO2 films on Si substrate

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3.1.3 Surface morphology study

As shown in Fig. 4a–c, XPS analysis was used to investigate the surface elemental and bonding states of the prepared Si3N4, ZrO2, and Si3N4:ZrO2 films on the Si substrate using single chromatic Al Kα radiation (1486.6 eV). To calibrate all the peaks, we used the C 1s peak, which has a binding energy of 284.5 eV. In Fig. 4a, the significant peaks of the survey spectrum correlate with the N, Si, and O in the film. The presence of Si–N bonds can be observed in the narrow-scan XPS spectra of Si 2p and N 1s (insets of Fig. 4a). This is because the main peak in the Si 2p spectrum centered at 101.7 eV is assigned to the Si–N bonds. The dominant peak in the N 1s spectrum centered at 398 eV is due to the N–Si bonds [49]. The core-level Zr 3d spectrum reveals two spin–orbit elements with an energy split of 2.4 eV, the Zr 3d5/2 peak with a binding energy of 183.36 eV verifies that the oxidation state is Zr4+ [30], and the peak of Zr 3d3/2 is positioned at 185.67 eV, as shown in the insets of Fig. 4b. The prominent peak at 530.6 eV in the O 1s spectra is attributed to the Zr–O bond in ZrO2 [34]. Further, Fig. 4c shows the XPS survey spectrum and elemental splitting of the Si3N4:ZrO2 (double interlayer) films. The presence of Si, Zr, N, and O was observed. The small peaks in Fig. 4a–c are attributed to C, Ar, and O. Ar peaks appeared because of surface cleaning prior to the XPS measurements. However, the C and O peaks originate may be due to the residual surface contamination and/or residual atmospheric gases in the sputtering chamber [35, 50].

Fig. 4
figure 4

a–c A typical survey scan XPS spectrum of the samples, the insets show the narrow-scan XPS spectra of the a Si 2p and N 1s: b Zr 3d5/2, Zr 3d3/2, and O 1s: c Si 2p, N 1s, O 1s, and Zr 3d energy level

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3.1.4 SEM–EDX analysis

SEM was used to investigate the morphology of the Si3N4, ZrO2, and Si3N4:ZrO2 (single and double interlayer) films (Fig. 5a, c, e). A homogeneous surface with small equiaxed grains is observed on all films, indicating that the RF-magnetron sputtered single and double interlayer films are uniform, densely packed, accurate on the surface, and exhibit island growth. The EDX spectra of the single-and double interlayer films indicate the existence of N, O, and Si in (Fig. 5b), Zr, O, and Si in (Fig. 5d), and Zr, Si, N, and O in (Fig. 5f). The thicknesses of the deposited films were determined using cross-section SEM. Even though we deposited two layers on the substrate, the Si3N4:ZrO2 layer thickness was 80–100 nm. Figure 5g shows the cross-section of the double interlayer film. The grain size of the double interlayer film was larger than that of the single layer. The XRD, XPS, SEM, and EDX results confirmed the formation of Si3N4:ZrO2 uniform thin films on an n-Si substrate using sputtering, and the results are presented in Table 2.

Fig. 5
figure 5

SEM images and EDX spectrum of a, b for Si3N4, c, d for ZrO2, e, f, g for Si3N4/ZrO2 films on Si substrate

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Table 2 Elemental ratio analyses for the Si3N4, ZrO2, and Si3N4:ZrO2 films on Si substrate
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3.1.5 AFM analysis

Using AFM measurements, we studied the surface topography of the Si3N4 and ZrO2 films. And the 2D and three-dimensional (3D) topographic pictures from AFM, and the related surface roughness histogram (area = 3 μm × 3 μm) of the Si3N4, and ZrO2 single layer s, and Si3N4:ZrO2 double interlayer on n-Si, are shown in Fig. 6a–i. AFM 2D-pictures2D pictures spherical-shaped grains that are homogeneous, continuous, and dense (Fig. 6a, d, g). The 3D images in Fig. 6c, f, i show a combination of the microscopic particles in establishing a homogeneous distribution on the n-Si substrate. From Fig. 6b, e, h, the (Ra) average roughness and root mean square (RMS) of Si3N4, and ZrO2 single layers and Si3N4:ZrO2 double interlayer on n-Si was 0.67, 1.25, and 1.32 nm, and 0.875, 1.589, and 1.662, respectively. The surface topology of the prepared films is significantly influenced by the double interlayer [51, 52]. The film thickness was projected to increase when two insulating layers were added, resulting in improved electrical characteristics of the films. Consequently, the topological results were consistent with the XRD, XPS, and FESEM analyses.

Fig. 6
figure 6

a, d, g 2D surface morphology. b, e, h height profiles of 2D surface morphology, c, f, i 3D surface morphology of Si3N4, ZrO2, and Si3N4/ZrO2 films on Si substrate through AFM

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3.2 Evaluation of electrical characteristics of MS diode, MIS, and MIIS SDs

3.2.1 I–V characteristics of MS diode, MIS, and MIIS SD

To correlate the structural investigations of Si3N4 and ZrO2 with the electrical characteristics, we prepared Mo/Si3N4/n-Si, Mo/ZrO2/n-Si MIS (single layer), Mo/Si3N4/ZrO2/n-Si MIIS (double interlayer) SDs, and a Mo/n-Si as the standard MS SD as shown in Fig. 7; Fig. 1 shows the schematic structure of these SDs. The prepared Mo/Si3N4/ZrO2/n-Si SDs exhibited good rectifying behavior. For the applied forward/reverse bias voltage, the current through the MIIS SD was significantly lower than that of the MIS and standard MS diodes. Figure 7 depicts the usual current–voltage (I–V) properties of the MS, MIS, and MIIS SDs. Compared with the MS diode, both the single (MIS) and double (MIIS) interlayer SDs demonstrated superior rectification. Compared to the Mo/n-Si diode (6.57 × 10−6 A at − 1 V), the reverse current leakages recorded in the Mo/Si3N4/n-Si (1.83 × 10−7 A at − 1 V) and Mo/ZrO2/n-Si SDs (1.21 × 10−8 A at − 1 V) were much lower. Compared to the SD and single layered SDs, the reverse current leakage of the Mo/Si3N4/ZrO2/n-Si SD (1.95 × 10−9 A at − 1 V) is significantly lower, which could be due to the potential barrier estimated by selecting insulating layers between the metal (Mo) and semiconductor (n-Si). Furthermore, thermionic emission (TE) theory was used to evaluate the I–V characteristics, the current through the SD with the effect of RS and an interlayer at forward bias (V > 3kT/q) is determined by the following relationship [53].

$$\mathrm{I}={\mathrm{I}}_{0}\mathrm{exp}\left[\frac{\mathrm{q}\left(\mathrm{V}-{\mathrm{IR}}_{\mathrm{s}}\right)}{\mathrm{nkT}}\right]\left\{1-\mathrm{exp}\left[\frac{\mathrm{q}\left(\mathrm{V}-{\mathrm{IR}}_{\mathrm{S}}\right)}{\mathrm{kT}}\right]\right\}$$
(2)

where IRS, V, T, q, k, n, and I0, A, A*, and Φb has conventional meanings [1, 2]. The reverse saturation current (I0) is obtained from the intercept of the plot of ln I versus V at V = 0, given by

Fig. 7
figure 7

Typical I–V characteristics of the fabricated Mo/n-Si (MS) SD, Mo/Si3N4/n-Si, Mo/ZrO2/n-Si (MIS), Mo/Si3N4/ZrO2/n-Si (MIIS) (single layer and double layer) SDs

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$${\mathrm{I}}_{0}={\mathrm{AA}}^{* }{\mathrm{T}}^{2}\mathrm{ exp}\left(-\frac{\mathrm{q}{\Phi }_{\mathrm{b}}}{\mathrm{kT}}\right)$$
(3)

After determining the saturation current I0, the Φb can be calculated using the expression

$${\Phi }_{\mathrm{b}}=\frac{\mathrm{kT}}{\mathrm{q}}\mathrm{ ln}\left(\frac{{\mathrm{AA}}^{*}{\mathrm{T}}^{2}}{{\mathrm{I}}_{0}}\right)$$
(4)

The ideality factor (n) values measures the diode’s conformity to pure TE, it is determined using the relationship from the slope of the linear region of forward bias ln I–V.

$$\mathrm{n}=\frac{\mathrm{q}}{\mathrm{kT}} \left(\frac{\mathrm{dV}}{\mathrm{d}\left(\mathrm{lnI}\right)}\right)$$
(5)

The on/off ratio, barrier height (BH), ideality factor (n) of the Mo/n-Si SD are 102, 0.71 eV, 1.23, respectively, whereas those of Mo/Si3N4/n-Si and Mo/ZrO2/n-Si SDs are 105, 0.88 eV, 1.65, and 105, 0.99 eV, 1.31, respectively. Compared to the MS diode and MIS (single layer) SDs, the on/off ratio, BH, and n of the Mo/Si3N4/ZrO2/n-Si (double interlayer) SD increased to 106, 1.04 eV, and 1.75, respectively. The successful reduction of n-type defect growth through the deposition of the insulator layer in the MIIS SD is attributed to the increased BH values [54, 55, 65]. Furthermore, negative charges are more prevalent in MIIS and MIS SDs than in MS diodes, which can be ascertained to the electron traps formed at the Si junction and then strongly associated with Si vacancies formed closer to the substrate surface during double-interlayer deposition [56].

3.2.2 Cheung’s mechanism of MS diode and MIS SDs

Determining BH, and n from the nonlinear region of the I–V graph is not accurate. Therefore, Cheung mechanisms are used to calculate the BH, n, and series resistance (RS) from the nonlinear region of the forward basic I–V graph, similar to the mechanism utilized in our earlier study [48]. Figure 8a–c show the graphs of dV/d(lnI)–I and H(I)–I for the MS SD, the MIS single layer, and MIIS double interlayer SDs, respectively. The slope of the plot of dV/d(lnI)–I is RS, and the y-axis intercept is nkT/q, which is associated with the n values. Using the n values obtained from the dV/d(lnI)–I graph, RS and BH are calculated using the slope and y-axis ordinate via linear curve fitting. From the dV/d(lnI)–I graph, the RS and n values of the MS diode are 64 Ω and 1.16, respectively. The BH and RS values for the MS diode are 0.72 eV and 63 Ω from the H(I)–I graph (Fig. 8a). The RS and n values for Mo/Si3N4/n-Si, Mo/ZrO2/n-Si, and Mo/Si3N4/ZrO2/n-Si SDs have been calculated to be 3946 and 1.75, 7711 Ω and 1.65, and 3602 Ω and 1.28, respectively, from the dV/d(lnI)–I graph (Fig. 8b). The values of BH and RS obtained from the H(I)–I plot in Fig. 8c for the Mo/Si3N4/n-Si, Mo/ZrO2/n-Si, and Mo/Si3N4/ZrO2/n-Si SDs are 0.82 eV and 4193 Ω, and 1.00 eV and 7271 Ω, and 1.12 eV and 2675 Ω, respectively. The I–V technique agreed well with the BH values calculated using Cheung’s method. Furthermore, the values of RS calculated from the dV/d(lnI)–I graph are identical to the values calculated from the H(I)–I graph, demonstrating that Cheung’s method is accurate. Furthermore, the values of RS of the MIS and MIIS SDs are larger than those of the MS diode. This discrepancy implies a decrease in the rapidly increased rate of the current induced by the injection of space charge into the Si3N4 and ZrO2 insulating layers at a higher voltage. Furthermore, compared to the values obtained using the I–V technique, the values of ideality factors calculated using Cheung’s functions are higher. This demonstrates the presence of effects like RS and BH according to the voltage drop across the interface states and the interface layer with applied bias in the low region of voltage in the (I–V) graph [57, 66, 67].

Fig. 8
figure 8

a dV/d(lnI)–I, and H(I)–I plots for the Mo/n-Si (MS) SD, b, c for the Mo/Si3N4/n-Si, Mo/ZrO2/n-Si(MIS), Mo/Si3N4/ZrO2/n-Si (MIIS) (single layer and double layer) SDs

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3.2.3 Norde’s technique of MS diode and MIS SDs

Further, the RS and BH of the MS SD, MIS, and MIIS SDs were calculated from the techniques described by Norde (Fig. 9a) [58], which were also used in our earlier study [16]. The BH and RS values for Mo/n-Si diode, Mo/Si3N4/n-Si, Mo/ZrO2/n-Si, and Mo/Si3N4/ZrO2/n-Si SDs are 0.73 eV and 94 Ω, 0.89 eV and 159 k Ω, 1.02 eV and 2096 k Ω, and 1.16 eV and 53 M Ω, respectively. The values of BH calculated using Norde’s method were larger than those calculated using the FB I–V plot, which could be attributed to the deviations from the ideal TE caused by the presence of an interlayer at the interface. Norde’s technique may not be appropriate for rectifying junctions with a high ideality factor. Consequently [16, 69], the BH, and RS values evaluated using Norde’s technique are higher than all the calculated from Cheung functions, which could be owing to Norde’s plot resultant values calculated from a full part of the FB I–V data of SDs.

Fig. 9
figure 9

a F(V)–V, b ΨSP–V plots for the Mo/n-Si (MS) SD, Mo/Si3N4/n-Si, Mo/ZrO2/n-Si(MIS), Mo/Si3N4/ZrO2/n-Si (MIIS) (single layer and double layer) SDs obtained from forward I–V characteristics

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3.2.4 Chattopadhyay mechanism of MS diode, MIS, and MIIS SDs

A negative oxide layer forms on the semiconductor surface when the metal and semiconductor come into direct contact [59]. The BH values can be calculated using the critical surface potential ΨSP (IC, VC), where VC is the critical voltage, and n = 1/α as the experimental value [46, 48, 60]. Further, ΨSP value can be determined using an equation and a process utilized in our previous study [8]. For the MS SD, MIS, and MIIS SDs, the calculated BH, ‘n’ values are 0.71 eV, 0.92 eV, 0.91 eV, and 0.98 eV for BH, and 1.19, 1.81, 1.57, and 1.45 for n, as shown in Fig. 9b. The FB I–V, Cheung’s, Norde’s, and ΨSP-V methods yielded almost identical BH values. Therefore, the methods used in this study produce accurate and effective results. Table 3 summarizes the electrical properties of the MS SDand the MIS and MIIS SDs. The BH value of the double interlayer MIIS SDincreased compared to the single layer MIS SD, as shown in Table 3. This is because Zr, N, and O react with Si, resulting in the development of interfacial Zr–O–N and Zr-Si phases at the interface (as shown using XRD Fig. 3, XPS Fig. 4, and EDX Fig. 5). This is due to the changes in non-stoichiometric impurities near the interface, which increased BH. Another factor is that the development of these phases may induce vacant states in n-Si at the interface, which behave as deep acceptor states, causing an increase in BH when a double interlayer on the Si substrate. All Schottky barrier characteristics derived from Figs 7, 8, 9 using different methods were compared to the values in previous literature [29, 35, 41, 60, 63,64,65] and are listed in Table 3.

Table 3 Parameters determined from the forward and reverse bias I–V characteristics of the MS, MIS SDs, and MIIS SDin the present work, and comparison with the previously reported MIS Schottky and heterostructures in the literature
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3.2.5 Forward bias (FB) current transport mechanism

A log (I)–log (V) plot is shown in Fig. 10a to identify the current conduction/transport mechanism in the entire FB region of the Mo/n-Si (MS) SD and Mo/Si3N4/n-Si, Mo/ZrO2/n-Si (MIS), and Mo/Si3N4/ZrO2/n-Si (MIIS) (single layer and double interlayer) SDs. The log (I)–log (V) plot for both diodes at different linear regions (region I, II, and III) with typical power exponents of formula IαVm and the slope of the linear fit to the conduction mechanism plot can be used to calculate the exponential value m in this case. The results for regions I, II, and III are presented in Table 4. The values in a region I are close to unity, indicating that the current follows a linear relationship with I–V. This indicates that at low voltages, the current transmission affects Ohm’s law, with background doping and thermally evolved carriers predominating over the injected charge carriers [8, 68]. The current gradually increases in the intermediate stage (region II). In region II, slope values greater than 2 indicate that the space-charge-limited current (SCLC) may dominate the current transport mechanism. However, the voltage in this region becomes more prominent than in region I, and the injected free charge carrier density is significantly higher than the thermally generated free charge carrier density [56]. The slope values tend to increase when the diode approaches the trap-filled limit current, whereas the injection level is high, with the same dependence as the trap-free SCLC [16].

Fig. 10
figure 10

a FB log(I)–log(V), b ln (IR)–V1/2 plots for the Mo/n-Si (MS) SD, Mo/Si3N4/n-Si, Mo/ZrO2/n-Si(MIS), Mo/Si3N4/ZrO2/n-Si (MIIS) (single layer and double layer) SDs

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Table 4 Forward conduction mechanism results of the MS SD, MIS, and MIIS SDs
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3.2.6 Reverse bias current conduction mechanism

As shown in Fig. 10b, the reverse bias leakage current (IR) of the MS SD, MIS, and MIIS SDs has an exponential relationship with the reverse bias voltage (VR), indicating that the Poole–Frenkel emission (PFE) and Schottky emission (SE) mechanisms were active in the diodes. That is, regardless of the 2D-insulating layer, the ln (IR)–VR1/2 plot (Fig. 10b) shows a linear change, implying that the reverse current will occur by the PFE or SE for all diodes. The reverse current owing to the PFE is described using the following equation [16, 61, 68].

$${I}_{R}={I}_{o}exp\left(\frac{{\beta }_{PF}\sqrt{V}}{{K}_{B}T\sqrt{d}}\right)$$
(6)

The current is determined by SE, and it may be calculated using

$$IR=A{A}^{*}{T}^{2}exp\left(\frac{{-}_{{\Phi }_{b}}}{kT}\right)exp\left(\frac{{\beta }_{SE}\sqrt{V}}{{k}_{B}T\sqrt{d}}\right)$$
(7)

where βPFE and βSE are the field-lowering coefficients of PFE and SE, respectively. The theoretical βPF and βSE values are as follows:

$$2{\beta }_{SE}={\beta }_{PF}=\sqrt{\left(\frac{{q}^{3}}{{\pi \varepsilon }_{o}{\varepsilon }_{r}}\right)}$$
(8)

βPF is always twice the value of βSE in most cases. The theoretical field-lowering coefficients for the MS diode are βPF = 2.209 × 10−5 eV m1/2 V−1/2 and βSE = 1.10 × 10−5 eV m1/2 V−1/2, whereas the theoretical values of the MIS SD are βPF = 9.53 × 10−5 eV m1/2 V−1/2 and βSE = 4.77 × 10−5 eV m1/2 V−1/2. The experimental and equivalent values were extracted from the slope of the linear fitting of the ln (IR)–VR1/2 plot. The calculated values for the Mo/n-Si SD is 1.99 × 10−5 eV m1/2 V−1/2 which is closely matched to the theoretical values of SE. It is therefore hypothesized that SE is the predominant charge conduction mechanism for the Mo/n-Si SD. Two distinct linear regions are readily seen in the plots of ln (IR)–VR1/2 for the MIS and MIIS SDs (I and II; Fig. 10b). The experimentally determined slope values for the Mo/Si3N4/n-Si, Mo/ZrO2/n-Si, and Mo/Si3N4/ZrO2/n-Si SDs were 6.6 × 10−5 and 1.87 × 10−5, 5.25 × 10−5 and 2.21 × 10−5, and 7.26 × 10−5 and 2.55 × 10−5 eV m1/2 V−1/2, respectively. In the plots for the MIS and MIIS SDs, region I slope values (lower bias) were near to the theoretical values of βPF, while region II slope values (higher bias) were close to the theoretical values of βSE. This research shows that at lower biases the PFE mechanism controls reverse current conduction, while at higher biases SE is in control. SE involves current conduction via the contact interface as opposed to the bulk material because of the non-uniformity and native oxides of the insulating layers (Si3N4, ZrO2 and Si3N4/ZrO2). In the PF conduction mechanism, there is a wide distribution of traps in the insulating layer's bandgap that are caused by deficiencies or residues in the combination of the material. This might be the cause of the improved charge carrier trapping or detrapping performance [62, 63].

3.2.7 Energy band diagram

We suggest a mechanism for BH control for the Mo/n-Si (MS) SD, Mo/Si3N4/n-Si, Mo/ZrO2/n-Si (MIS), and Mo/Si3N4/ZrO2/n-Si (MIIS) (single layer and double interlayer) SDs using the BH values calculated from I–V, Norde’s, Cheung’s, and Chattopadhyay’s methods. Figure 11 shows a reliable energy band diagram of the MS SDand the MIS SD. Metal-induced gap states (MIGS) have pinned Fermi values at metal-semiconductor (SC) SDs [8, 16]. When a metal wave function decays into the SC and crates the MIGS, it results in the pinning of Fermi levels at the device interface [37, 64]. This could explain the permeation of free states into the metal electrode at contact (Fig. 11a). By restricting the metal wave function entry into the SC bandgap and doping the free states, an insulating layer can decrease the Fermi level pinning generated by the MIGS. Si3N4 and ZrO2 acted as interlayers in this study (Fig. 11b), restricting free states at the actual MIS interface. Consequently, the effective BH values of the MIS and MIIS SDs increased.

Fig. 11
figure 11

Possible energy level band diagrams of the a MS SD and b Mo/insulating layer/n-Si SDs with free states, χS is electron affinity of semiconductor, Eg is energy band gap, ɸb is barrier height, ɸm is a metal work function, EF is Fermi energy level, EV is valence and EC is CBs

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4 Conclusion

High-quality wide bandgap and high-k Si3N4 and ZrO2 films were effectively deposited on n-Si using thermal evaporation, DC, and RF-magnetron sputtering systems. Their optical, structural, morphological, and chemical properties were studied. The entire UV/Vis region of the electromagnetic spectrum was responsive. XRD results showed high-intensity refractions of the ZrSiO4 (2 0 0), Zr2ON2 (4 0 0), Zr7O11N2 (1 2 8), and ZrSi2 (1 7 1) planes. XPS results indicated that the Si 2p spectrum centered at 101.7 eV was assigned to Si–N bonds, Zr 3d5/2, and Zr 3d3/2 peaks at 183.36 eV and 185.67, and O 1 s at 530.6 eV were attributed to the Zr–O bond in ZrO2, and the presence of Si, Zr, N, and O were observed. The SEM images showed that the films were uniform, densely packed, and accurate on the surface, and EDX spectra confirmed the existence of Zr, Si, N, and O. AFM analysis showed that the overall surface morphology of all the films on n-Si was smooth. UV–VIS, XRD, XPS, SEM–EDX, and AFM investigations confirmed that Si3N4 and ZrO2 films were formed on the n-Si substrate. Subsequently, Mo/Si3N4/n-Si, Mo/ZrO2/n-Si (MIS), and Mo/Si3N4/ZrO2/n-Si (MIIS) (single layer and double interlayer) SDs were fabricated, and their electrical properties were characterized through forward and reverse biased current–voltage (I–V) measurements at ambient temperature. The electrical characteristics were compared to those of a standard Mo/n-Si (MS) SD. Compared with the MS SD, the MIS SDexhibited good rectification properties and low reverse current leakage. The BH values estimated in MIIS SDwere higher than in MIS SDs and MS diode. In addition, Cheung’s, Norde’s, and Chattopadhyay’s methods were used to compare the calculated BH, n, and RS values of the MS, MIS SDs and MIIS SD. Energy-level band diagrams were used to describe the BH modulation method. According to the FB I–V characteristics, the MS, MIS, and MIIS diodes were ohmic in the lower bias region and SCLC in the high-voltage region. The reverse leakage current in the MS diode is therefore hypothesized that SE is the predominant charge conduction mechanism. The MIS and MIIS SDs shows two regions (lower and higher), in lower biases the PFE is the dominant reverse current conduction, while at higher biases SE is in dominant current conduction mechanism. Furthermore, Si3N4 and ZrO2 are appropriate insulating layer materials for innovative optoelectronic device applications.