1 Introduction

A metal-polymer-semiconductor (MPS) structure is made by sandwiching a polymer/organic film between M and S. The electrical and dielectric behaviors of MPS structure are almost identical those of devices such as MIS and MOS devices [1,2,3,4,5]. As with Schottky barrier diode (SBD), MPS device indicates rectifier behavior. Polymer thin films as gate insulators are often used in different devices like batteries, solar cells, transistors, sensors and light-emitting diodes. Polymers obtained by simple solution techniques are highly attractive for these devices. Polymers like polyvinyl-pyrrolidone (PVP), polyvinyl alcohol (PVA), polyaniline (PANI) and polypyrrole (PPy) are another group of vinyl polymer. Polymer thin films can be prepared using various techniques such as drop-coating, dip-coating, ink printing, spraying, electrospinning, and spin coating [6,7,8]. Electrospinning and spin coating technique is one of the important techniques used to obtain high quality polymer thin films. Polyvinylpyrrolidone (PVP) is a highly polar and an amorphous polymer. PVP has important and useful properties like good easy processability, very low toxicity, high water solubility, good film-forming, good thermal and mechanical stability [8,9,10,11]. PVP is also used in ceramic, electrical, metallurgical, and pharmaceutical industry, various cosmetics, adhesives, and coatings.

Cobalt-ferrite (CoFe2O4) is a spinel ferrite such as MgFe2O4, MnFe2O4, and ZnFe2O4. Among these ferrites, the cobalt ferrite has excellent physical and chemical properties like good stability, high coercivity, good mechanical hardness, strong anisotropy, and moderate saturation magnetization [12,13,14,15,16,17,18,19]. It has a cubic spinel structure and is a magnetic material. The cobalt ferrite is used in various applications digital recording disks, storage devices, magnetic and switching devices, transformers, audio, and videotape.

In the present work, the electrospinning method was used for the deposition of polymer thin film on n-Si wafer. Then, the MS diodes with and without CoFe2O4-PVP interlayer were prepared by forming ohmic and rectifier contacts. The main electronic parameters of them were calculated by using various methods such as Thermionic Emission (TE) and Norde.

2 Experimental

2.1 Preparation of CoFe2O4 Nanostructures

For preparation of CoFe2O4 nanostructures, 0.1 M of cobalt acetate (from Loba Chemie Company) was dissolved in deionize-water (DW) as cobalt source and in another backer, 0.1 M of Iron chloride (FeCl2) was dissolved in the same procedure in double distilled water, both of anionic and cationic precursors were mixed in a rounded bottom backer and kept under ultrasonic waves for 15 min, the ultrasonic irradiation was not continued process. Every 5 min, the ultrasonic process was stopped for 5 min. After that, the prepared suspension was centrifuged and washed with distilled water for several times, and eventually, the material dried in the open air, and then the as-utilized powder was annealed in an ordering oven for 60 min and then it was characterized by XRD.

2.2 The Fabrication Process of MS and MPS Diodes

To fabricate the MS diodes with and without CoFe2O4-PVP interlayer, the n-Si wafer having (100) orientation and resistivity of 1–10 Ωcm is used. Firstly, it was dipped in ammonium-peroxide ((NH4)2O2) to remove organic contamination and native oxide on the surface of wafer and then it is etched using various acidic and basic chemical solutions. The chemically cleaned wafer is rinsed in ultra-pure deionized water and dried with pure-N2 gas. Consequently, ohmic and rectifier contacts to be used for electricity transmission were formed. For ohmic contact with about 1500 Å thickness, high-pure Au was grown as thermally onto back-side of wafer at 10−6 Torr and then the wafer was annealed at 550 °C for 5 min under N2 atmosphere. For rectifier contact with about 1500 Å thickness, Au rectifier contacts with 1 mm diameter were grown on the first quarter of the wafer. Thus, Au/n-Si (MS) diode was completed. To grow the (CoFe2O4-PVP) interlayer on the second quarter wafer, electrospinning method was used and then the same Au rectifier contacts were grown on the interlayer. Thus, Au/(CoFe2O4-PVP)/n-Si (MPS) diode was fabricated. The I–V and C/G–V measurements were carried out by using Keithley 2400 and HP 4192A LF, respectively.

3 Result and Discussion

3.1 CoFe2O4 Nanostructure Analysis

Figure 1 shows the XRD pattern of the prepared powders, which depicted cubic CoFe2O4 crystalline structure. The broadness of the peaks confirms the nano-dimension of the product. There are no other peaks in the pattern, and it shows the purity of CoFe2O4 nanostructures.

Fig. 1
figure 1

XRD pattern of CoFe2O4 nanostructures

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Figure 2a and b show field emission scanning electron microscopy (FE-SEM) images of the nanostructures with different magnifications. The morphology of the nanostructures is semi-plate and has a formed in the form of polydispersive cluster nanostructures of less than micron size. For the chemical characterization of CoFe2O4 nanostructures, the energy dispersive X-ray (EDX) analysis was used to recognize the presented elements in the prepared Nano powder. The results of the EDX analysis are shown in Fig. 2b. The observed a sharp peak of Oxygen(O) with a weight percentage of 61.1, Cobalt (Co) with a weight percentage of 21.0 is detected together with the peak of Ferrite (Fe) with a content of 17.9 wt%.

Fig. 2
figure 2

FE-SEM image in different magnifications. a 70 kx, b EDX profiles of CoFe2O4 nanostructures

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Optical properties of prepared nanostructures were analyzed in the range of 200–800 nm. Optical absorption was used to evaluate the energy gap of the nanostructures shown in Fig. 3. As can be seen from Fig. 3, the nanostructures have low absorbance in the visible regions and high absorbance in the ultraviolet region.

Fig. 3
figure 3

UV–Vis absorption spectra for CoFe2O4 nanostructures

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3.2 I-V Characteristics of the MS and MPS Diodes

The conventional IF-VF method was used to extract basic diode parameters like saturation current (Io), ideality factor (n) and barrier height (ΦB0) of the fabricated MS diode with/without (CoFe2O4-PVP) interlayer. These diodes obeying the TE theory (V ≥ 3kT/q) is described by the following relations [20, 21],

$$I = I_{o} \left( {{\exp}\left( {\frac{{q\left( {V - IR_{s} } \right)}}{nkT}} \right) - 1} \right)$$
(1)

Both the values of Io and n are extracted from the intercept and slope of the linear part of the semi-logarithmic IF-VF plot, and they are given as follows, respectively,

$$I_{o} = AA^{*} T^{2} {\exp}\left( { - \frac{{q\phi_{B0} }}{kT}} \right)$$
(2)
$$n = \frac{q}{kT}\left( {\frac{dV}{{d\left( {{\text{In}} I} \right)}}} \right)$$
(3)

Thus, ΦB0 value can be obtained from the Eq. (2).

Figure 4 illustrates Ln(IF)-VF curves of the MS and MPS diodes and the fabricated devices show diode-like behavior. It is clear that I–V curves of these diodes indicate a strongly rectifying behavior. The rectifying-rate (RR) which is the ratio of the current for positive and negative voltage, of the MS and MPS diodes was found as 6.44 × 102 and 3.43 × 103 at ± 3, respectively. As a result, the used (CoFe2O4-PVP) interlayer leads to the increase RR value.

Fig. 4
figure 4

The Ln(IF)-VF curves of these diodes

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At low voltage, Ln(IF)-VF curves exhibit a linear behavior. The obtained I0, n and ΦB0 values of the MS and MPS diodes are presented in Table 1. It is seen that the obtained n and ΦB0 value of MPS is higher than MS diode. This result is due to the CoFe2O4-PVP interlayer. Besides, the obtained n value has greater than unity. For an ideal Schottky diode with current-dominated by TE, the n value must be equal to unity. The obtained high values of n can be caused by the Rs, non-homogeneous barrier, tunneling-current, existence of interlayer and Nss [20,21,22,23,24,25,26,27,28]. In addition, at higher voltages, the I–V curves deviate from linearity due to the Rs.

Table 1 The determined electronic parameters of these diodes
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To obtain the values of series resistance and shunt resistance (Rsh) of these diodes, Ohm’s law \(({\text{R}}_{{\text{j}}} = \partial {\text{V}}/\partial {\text{I}})\) was used. Figure 5 illustrates the diode-resistance (Rj)-V curves of these diodes. Since the Rj-V curve becomes almost constant value for the high-reverse biases, the calculated value corresponds to the Rsh and it was found to be 1.90 MΩ and 4.47 MΩ at − 3 V for MS and MPS diode, respectively. If the Rj-V curve shows almost constant value in the forward bias region, the calculated value corresponds to the Rs. The Rs values were found to be 2.95 kΩ and 1.30 kΩ at + 3 V, respectively.

Fig. 5
figure 5

The Rj-V curves of these diodes

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After determining the n and ΦB0 from the I–V characteristic using TE theory, Norde method was used as another approach to extract the ΦB and Rs [29]. In this approach, Norde function, F(V), is given as:

$$F\left( V \right) = \frac{V}{\gamma } - \frac{kT}{q}\left[ {\ln \left( {\frac{I\left( V \right)}{{AA^{*} T^{2} }}} \right)} \right]$$
(4)

In Eq. 4, γ is an integer greater than n value. Accordingly, the ΦB and Rs are given as follows,

$$\Phi_{B} = F\left( {V_{min} } \right) + \frac{{V_{min} }}{\gamma } - \frac{kT}{q}$$
(5)
$$R_{s} = \frac{{kT\left( {\gamma - n} \right)}}{{qI_{min} }}$$
(6)

This method includes F(V) plotted against voltage (V). This plot must give a distinctive minimum point, F(Vmin). Vmin and Imin are voltage and current values corresponding the F(Vmin), respectively. Figure 6 shows F–V curves of these diodes. It is observed that these plots has a minimum point. The extracted ΦB and Rs values are also tabulated in Table 1 and the value of BH obtained from Norde and TE theory are in good agreement with each other.

Fig. 6
figure 6

F(V)-V curves of these diodes

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To extract the density of Nss for two type diodes, the approach proposed by Card and Rhoderick [30] was used. In this method, the energy distribution profile of Nss is obtained with the help of the IF-VF characteristics. The unit of Nss is eV−1.cm−2, and the Nss is given as,

$$N_{ss} \left( V \right) = \frac{1}{q}\left[ {\frac{{\varepsilon_{i} }}{\delta }\left( {n\left( V \right) - 1} \right) - \frac{{\varepsilon_{s} }}{{W_{D} }}} \right]$$
(7)

In this equation, δ and WD are the interlayer thickness and depletion layer width determined from C−2–V curve as following section, respectively. Besides, εi and εs are the permittivity of the interlayer and semiconductor, respectively. The conduction band edge energy (Ec) with respect to the surface state energy (Ess) for n-type semiconductor is given by [21, 30],

$$E_{c} - E_{ss} = q\left( {\Phi_{e} - V} \right)$$
(8)

where Φe is the effective BH (ϕe) and is given as follows,

$$\Phi_{e} - \Phi_{B0} = \left( {1 - \frac{1}{n\left( V \right)}} \right)\left( {V - IR_{s} } \right)$$
(9)

Figure 7 shows the Nss vs (Ec-Ess) of the MS and MPS diodes. For MS and MPS diodes, the Nss values at about Ec = 0.47 eV are found to be 6.72 × 1013 eV−1 cm−2 and 6.24 × 1012 eV−1 cm−2, respectively. As can be seen in Fig. 7, Nss value of MPS diode is lower than the MS diode. This results from the passivated role of the interfacial layer or the saturation of dangling- bonds [31,32,33].

Fig. 7
figure 7

The energy distribution curves of Nss for these diodes

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In addition, the In(IF)-Ln(VF) plots were drawn to determine the current (CMs) for the two diodes, and represented in Fig. 8 and these curves were indicated three linear regions called as Region 1, 2, and 3 that obeys I α Vm relation. The m values were calculated from the slope of In(IF)-VF curves. For the three regions, the m values of MS diode were found to be 1.17, 3.89 and 4.11, respectively. For MPS diode, the m values were found to be 1.04, 7.56 and 4.16.

Fig. 8
figure 8

The double-logarithmic IF-VF curves of these diodes

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In the Region 1, the obtained m value for two diodes is close to unity. This result indicates that the CCM of these diodes exhibits an ohmic behavior. In other words, the CM is governed by Ohm’s law. In the Region 2, the obtained m value is larger than 2. This case shows that the CCM or current transport is governed by trap-charge limited current (TCLC) with an exponential trap distribution. In the Region 3, the dominant CCM is space charge limited current (SCLC) controlled by single dominating trap-level [34,35,36,37,38].

3.3 C-V and G/ω-V Characteristics of the MS and MPS Diodes

Both capacitance and conductance measurements were performed at wide range of bias voltages between − 2 V and + 4 V and 1 MHz. The surface states cannot follow the frequency of the ac signal and hence cannot any contribution the measured of them at high frequencies (f ≥ 500 kHz). Therefore, they cannot contribute to total capacitance [3, 20, 39,40,41,42,43,44]. Figure 9a and b demonstrate the C–V and G/ω-V plots of these diodes at 1 MHz, respectively. As seen in Fig. 9, the capacitance and conductance indicate a strong dependence on voltage. Also, the C value of MS diode is higher than MPS diode. This case is due to the interlayer, which causes a decrease in interface states.

Fig. 9
figure 9

Plots of a C–V and b G/ω-V of these diodes at 1 MHz

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Another technique for measuring series resistance (Rs) is the admittance method developed by Nicollian and Goetzberger and according to this method, Rs can be calculated as follow [45].

$$R_{s} = \frac{{G_{ma} }}{{G_{ma}^{2} + \left( {\omega C_{ma} } \right)^{2} }}$$
(10)

In Eq. 10, Gma and Cma represent the measured values of them at accumulation region, respectively. Figure 10 shows the plots of Rs-V of these diodes at 1 MHz, which has a peak at about 0.5 V. This peak is due to a special distribution of Nss located at (CoFe2O4-PVP)/n-Si interface and their relaxation or life time.

Fig. 10
figure 10

Rs-V plots of these diodes

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The values of Fermi-energy (EF), concentration of donor atoms (ND), diffusion-potential (VD = V0 + kT/q), WD and ΦB(C–V) of these diodes can be calculated from the C−2–V characteristic given in Fig. 11. The relation between capacitance and V is given as follows [20, 21, 46,47,48,49,50,51,52,53],

$$C^{ - 2} = 2\left( {V_{o} + V} \right)/\left( {q\varepsilon_{s} \varepsilon_{o} A^{2} N_{D} } \right)$$
(11)
Fig. 11
figure 11

The C−2–V plots of these diodes at 1 MHz

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The value of V0 and ND was extracted from the intercept and slope of the linear region of C−2–V plot. Other parameters given below were calculated using the V0 and ND values.

$$E_{F} = \frac{kT}{q}{\text{In}}\left( {\frac{{N_{C} }}{{N_{D} }}} \right),\;E_{m} = \left[ {\frac{{2qN_{D} V_{0} }}{{\varepsilon_{s} \varepsilon_{0} }}} \right]^{0.5} ,\;\Delta \Phi_{b} = \left[ {\frac{{qE_{m} }}{{4\pi \varepsilon_{s} \varepsilon_{0} }}} \right]^{0.5} \;{\text{and}}\;W_{D} = \sqrt {\frac{{2\varepsilon_{s} \varepsilon_{0} V_{D} }}{{qN_{D} }}}$$
(12)

Thus, the ΦB(C-V) can be calculated as follows,

$$\Phi_{{B\left( {C - V} \right)}} = V_{D} + \frac{kT}{q}{\ln}\left( {\frac{{N_{C} }}{{N_{D} }}} \right) - \Delta \Phi_{B} = V_{D} + E_{F} - \Delta \Phi_{B}$$
(13)

It is seen that these plots exhibit a good linear behavior in the inversion region. The calculated parameters are given in Table 2, and ΦB value of the MPS is higher than the MS diode. This is due to the existence of the (CoFe2O4-PVP) interlayer.

Table 2 The electrical parameters extracted from the C−2-V characteristics
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4 Conclusions

In this study, both the MS and MPS diodes were prepared on the same n-Si wafer to investigate the effects of (CoFe2O4-PVP) interlayer on the electrical characteristics by using I–V and C–V measurements. The values of I0, n and ΦB0 of these diodes were extracted from both TE and Norde methods. The observed a deviation from the linearity in Ln(IF)-VF and concave curvature in C–V curves at adequate high forward voltages was explained on the basis of Rs and native SiO2 and (CoFe2O4-PVP) interlayers because of the sharing of applied voltage by depletion layer, Rs, and interlayer. Also, the current conduction mechanisms of these diodes were investigated from the ln(IF)-ln(VF) which are obey IαVm relation. Additionally, the RR value for MS and MPS diodes was found as 6.44 × 102 for MS and 3.43 × 103 for MPS diode at ± 3,, respectively. The high value of the MPS diode is the result of the CoFe2O4-PVP interlayer. Similarly, the magnitude of Nss for MS and MPS diodes was found as 6.72 × 1013 eV−1 cm−2 and 6.24 × 1012 eV−1 cm−2, respectively. The low value of the MPS diode is caused by the passivation effect of interface states. The C–V and G/ω measurements indicate that both the C and G are dependent of voltage and interlayer. In addition, other electronic parameters of these diodes were determined from the C−2–V characteristics. The obtained results show that the interlayer, Nss and Rs can cause to significant effects both on the electrical characteristics of these MS and MPS diodes.