1 Introduction

MIS and MPS type electronic devices consist of an interfacial oxide and polymer layer between metal and semiconductor, and many defects or impurities may be occurred during the elaboration/fabrication of them. They are usually called as surface/interface states/traps (Nss/Dit) and may alter the performance of these devices. These states are usually originated from dangling bounds at surface of semiconductor and chemical composition of the interface [1,2,3,4,5]. The charges in these traps and dislocations may be stored or released under electric field [6,7,8,9]. Therefore, the value of admittance (Y = 1/Z = G + jωC) increases by decreasing frequency and these changes in them become more pronounced at lower frequencies depending on the life-times (τ) of the Nss and alternating ac signal. In other words, there are many types of the Nss with various lifetimes, especially at low-moderate frequencies [5,6,7,8,9,10].

The existence of a native/deposited interlayer such as insulator, ferroelectric and polymer at junction, MS structure is converted into the MIS, MFS and MPS structures. The thickness, its homogeneity and dielectric constant of interlayer are also more effective on the performance of these devices as much as barrier inhomogeneity [6,7,8]. Therefore, the n value acquired from the slope of forward bias Ln(I)–V curve becomes much higher than unity because of the existence of native or deposited interlayer, Nss, inhomogeneous of BH, and tunneling of charge carriers through BH [6,7,8,9, 11,12,13,14,15]. Therefore, main electrical of these structures obtained from the forward I–V based on TE theory and reverse bias C–V data may be considerably different depending on voltage, interlayer, and the nature of measured method. Therefore, in application, the obtained experimental results may be considerably different from the ideal case. Additionally, on the base of TE theory, the value of BH does not include the electric field and so the value of BH becomes a function of applied bias voltage [6,7,8, 16,17,18,19]. The magnitude of n is also an indicator of compliance to TE theory and its higher values imply a deviation from the TE theory (n ≈ 1) and it depend on various factors such as V, depletion layer width (Wd = ~ √1/N), the permittivity of interlayer (εi), and its thickness (di) [6,7,8]. The existence of many low-barriers at M/S interface, some low-energetic electrons can be tunneled via these barriers and cause an increment in n values.

Both the Rs and Rsh of electronic devices are also more effective on the conduction mechanism and then on the performance of them. In general, Rs may be rooted from the ohmic and Schottky contacts of the device, the used probe wires to get contacts, the resistance of the bulk semiconductor, and inhomogeneity doping atoms [7, 9]. But, the value of Rsh may be rooted from the physical defects, grain boundaries, and leakage current, and probe wires to the ground. Rs value can be determined by many methods from the I–V data. Among these methods, the commonly used ones which provide an opportunity for comparison are Ohm’s law [7], Norde [20] and Cheung functions [21], and modified Norde functions by Bohlin [22]. But, Ohm-law and Cheung functions are the easiest, exact and reliable ones from the high forward biases region because it realizes in this region and deviates from linearity of LnI–V plot and the bending of the C–V plot at accumulation region. According to Ohm’s law, the voltage dependence resistance of the structure (Ri = dVm/dIm) and Nicollian-Brews method (Ri = Gm/(G 2m  + (ωCm)2), can easy to calculate by utilizing the forward measured I–V and impedance (C–V and G/ω–V) data, respectively. But, the real value of Rs corresponds to high-forward biases and strong accumulation region of C/G–V plot, respectively.

The main aim of this study is to compare the basic electronic parameters of fabricated the Au/n-Si (MS) and Au/(Fe2O4-doped PVP)/n-Si (MPS) structures by considering the effects of (Fe2O4-doped PVP) organic layer, Nss, Rs, and their possible sources. For this aim, both the I–V and C/G–V (at 1 MHz) measurements were performed. In addition, the main electronic parameters of these two structures such as n, BH and Rs were obtained using the different methods, namely TE theory, Cheung’s and Nicollian-Brews methods and compared with each other. All these results confirm that the (Fe2O4-doped PVP) interfacial organic/polymer layer lead to a considerably decreases in Rs, Nss, leakage current and an increase in rectifying rate (RR), Rsh and BH when compared with reference device (MS).

2 Experimental details

In order to specify the effects of (Fe2O4-doped PVP) organic interlayer on the performance of the conventional MS structure, the Au/n-Si (MS) structures with and without this organic interlayer were performed on the P-doped (n-Si) wafer having (100) float zone, 350 μm thickness, 2” diameter, and ~ 1.078 × 1015 cm−3 dopant donor concentration atoms in same conditions. For the fabrication of the MS and MPS structures, two quarter n-Si wafers were dipped in ammonium-peroxide at 50 s to remove native-oxide layer and organic impurities on the two side of wafers and then wafers etched in the (H2SO4:H2O2:H2O = 3:1:1) solutions and (HCl:H2O = 1:1) for 1 min, respectively. After that, wafers rinsed in ultra-pure water and then N2 gas used for drying. After the cleaning processes, two quarter n-Si wafers were rinsed in deionized water and then dried in N2 gas. After that these two n-Si wafers were transferred into high-vacuum metal evaporation system and then 150 nm thickness of high-pure Au (99.999%) was evaporated onto the whole back side of the n-Si wafers at ~ 10−6 Torr. In order to get low-resistivity or good ohmic contact these two wafers were annealed at 550 °C for 5 min in a N2 atmosphere. Additionally, the current–voltage plots of them were measured by using Keithley-2400 source-meter and they show a good linear behaviour which is an evidence to perform a good ohmic contact. Then, high-pure Au circular dots with 1 mm diameter and 150 nm thickness were deposited on the front of first quarter n-Si wafer. In this way, the fabrication of Au/n-Si (MS) structures was completed. After that, utilizing electrospinning method, the growth of the prepared (Fe2O4-doped PVP) organic solution was realized on the front of second quarter n-Si wafer. The organic layer thickness was predicted as 22 nm from the interlayer capacitance (Ci). Immediately, high-pure Au (99.999%) circular dots with 1 mm diameter and 150 nm thickness were deposited on the (Fe2O4-doped PVP) organic layer at 10−6 Torr evaporation system. The schematic diagrams of them were also given in Fig. 1. The I–V and C/G–V measurements were realized by Keithley-2400 source-meter and HP4192A impedance analyser (5 Hz–13 MHz), respectively. All measurements were done by used a microcomputer through an IEEE-488 ac/dc converter card.

Fig. 1
figure 1

Schematic diagram of the Au/n-Si (MS) and Au/(Fe2O4-doped PVP)/n-Si (MPS) structures, respectively

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3 Results and discussions

3.1 Forward and reverse bias I–V characteristics

Figure 2 shows the semi-logarithmic I–V curves of the Au/n-Si (MS) and Au/(Fe2O4-doped PVP)/n-Si (MPS) structures between ± 3 V interval by 20 mV steps. As seen in the Fig. 2, the lnI–V curve for two structures exhibits typical diode behavior with a good rectifying rate. In addition, lnI–V plots have liner part in the intermediate forward bias voltage up to ∼ 0.5 V and then deviate from linearity because of the organic interlayer (Fe2O4-doped PVP) and Rs effects. Because, the applied biases across the structure will be shared by Rs, organic and depletion layers, but Rs effect at low and moderate bias voltages can be neglected low.

Fig. 2
figure 2

The semi-logarithmic I–V plots of the MS and MPS structures

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Since electronic devices have both Rs and n is greater than unity, TE theory can also be used to determine electrical parameters, and in this case the I–V relation (≥ 3 kT/q) is expressed as below [6,7,8].

$$I = AA^{*} T^{2} \exp ( - \frac{q}{kT}\varPhi_{Bo} )\left[ {\exp \left( {\frac{{q(V - IR_{s} )}}{nkT}} \right) - 1} \right] = {\text{I}}_{O} \left[ {\exp \left( {\frac{{qV_{D} }}{nkT}} \right) - 1} \right]$$
(1)

In Eq. 1, A* is the effective Richardson constant (112 A/cm2 K2 for n-Si), the products of IRs is the voltage drop across the Rs and the other quantities are most-known in the evaluable literature. Both Io and n values can be extracted from the intercepts and slopes of lnI–V plot [Ln(I) = Ln(Io) + (q/nkT)V] as following through the relation by using Eq. 1, respectively [6,7,8]:

$$n = \frac{q}{kT}\left( {\frac{dV}{d(\ln I)}} \right) = \left( {{\text{d}}_{\text{i}} /\varepsilon_{\text{i}} } \right)\,\left( {\varepsilon_{\text{s}} /{\text{W}}_{\text{d}} + {\text{qN}}_{\text{ss}} } \right)$$
(2)

Thus, ΦBo was extracted from Eq. 1 by using the acquired Io value and the diode area (A) for MS and MPS structures through the equation below [6,7,8].

$$\varPhi_{Bo} = \frac{kT}{q}Ln\left( {\frac{{AA^{*} T^{2} }}{{I_{0} }}} \right)$$
(3)

Io, n, ΦBo, and RR values were extracted from the Ln(I)–V plots as 2.9 × 10−8A, 1.699, 0.741 eV, and 1.45 × 104 for the MS and 2.30 × 10−9 A, 1.634, 0.806 eV, and 9.01 × 104 for MPS structure and they are tabulated in Table 1, respectively. It is clear that these values of n are higher than unity due to the lower BHs/patches at around mean BH, a spatial distribution of Nss at (Fe2O4-PVP)/n-Si interface, and organic layer. Many charge carriers (electron and holes) with low energies can easily pass across these patches and increase the n values. According to Saad and Kassis [23], the other reason of high value of n in these structures is the result of conduction dominated by interface recombination. The n value is a measure of TE theory and higher values of it deviates the structure from TE. The voltage dependent resistance (Ri = Vi/Ii) of these structures can be extracted from the Ohm’s law, but the real Rs value and Rsh of them corresponds to adequately high forward and reverse bias voltage. Therefore, the values of Rs and Rsh were calculated as 1.58 kΩ and 25.7 MΩ for MS and 1.17 kΩ and 103 MΩ for MPS at ± 3 V (Fig. 3), respectively.

Table 1 A comparison of some basic electrical parameters of the MS and MPS structures extracted from the Ln(I)-V and Cheung’s functions at room temperature
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Fig. 3
figure 3

The Ri–V plots of the Au/n-Si (MS) and Au/(Fe2O4-doped PVP)/n-Si (MPS) structures

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The main diode parameters (Io, n, ΦBo) can also be determined by using Cheung functions from the concave curvature forward bias region as following equations [21]:

$$\frac{dV}{{d\left( {In I} \right)}} = IR_{s} + \left( {\frac{nkT}{q}} \right)$$
(4a)
$$H\left( I \right) = V - \frac{nkT}{a}In\left( {\frac{I}{{AA^{*} T^{2} }}} \right) = IR_{s} + n\phi_{B}$$
(4b)

Both the dV/dIn(I) and H(I) versus I plots of two structures were drawn by using Eq. 4a and 4b, and were represented in Fig. 4a and b, respectively. As presented in Fig. 4a and b, related plots have a distinct linear behavior. Thus, as shown in Eq. 4a, the slopes and intercept points of the dV/dIn(I) versus I plots are exactly equal to the real Rs values and nkT/q. Thus, the value of Rs and n were found as 1.372 kΩ and 5.40 for MS and 1.266 kΩ and 4.40 for MPS structures, respectively. By using these values of n, H(I) versus I plots (Fig. 4b) were also drawn using Eq. 4b. The slopes and intercepts of these plots are corresponding to Rs and nΦB, respectively. Thus, both the values of Rs and BH were calculated as 1.32 kΩ and 0.606 eV for MS and 1.21 kΩ and 0.652 eV for MPS structure respectively. These values of n, Rs and Φb obtained by Cheung functions are in reasonably close agreement with each other. But, observed some discrepancy between these parameters obtained from TE theory and Cheung’s functions is the result of the voltage dependent of them and the nature of measurements methods.

Fig. 4
figure 4

dV/d(ln I) and H(I) versus I plots of the MS and MPS structures

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Figure 5 shows the double logarithmic IF–VF plots of two structures, which are related to the characteristic of the conduction process of dominant charge over the barrier. As shown in Fig. 5, the In(IF)–In(V) plot has three linear regions with different slopes and they called as I, II, and III which are correspond to low, intermediate and high forward bias voltages, respectively. It is clear that in these regions, Ln(IF)–ln(VF) plots have a power-law behavior (I ~ Vm+1) with different slope values (m) which is directly equal to the slope of these linear regions. Thus, the value of m for regions I, II, and III were found as 1.976, 3.915, and 1.846 for MS and 1.701, 5.002, and 2.144 for MPS structure respectively. Both in I and III regions for two structures, current-conduction is the space-charge-limited-current (SCLC) mechanism because m is closer 2, due to an increase in electrons injected from the electrode to the interlayer, and so leads to filling up of traps and a rise in space charges [24,25,26]. But, for region II m is larger than 2 for MS and MPS structure and so it has been interpreted as an indicator of trapped-charge-limited current (TCLC) with an exponential interface states/traps distribution.

Fig. 5
figure 5

Ln(IF–VF) plots of the Au/n-Si (MS) and Au/(Fe2O4-doped PVP)/n-Si (MPS) structures

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As shown in Fig. 2, the reverse bias IR–VR plots for these two structures have not a soft or non-saturation behavior and the values of IR increases with increasing VF or electric field. Such behavior of reverse bias current suggests that either Poole–Frenkel emission (PFE) or Schottky emission (SE) is dominant mechanisms in the MS and MPS structures. Therefore, ln(IR)–V 0.5R plots of them were drawn and given in Fig. 6 to determine possible current-transport mechanisms (CTMs/CCMs) in the MS and MPS structures.

Fig. 6
figure 6

Ln(Ir)–V 0.5R plots of the Au/n-Si (MS) and Au/(Fe2O4-doped PVP)/n-Si (MPS) structures

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According to the PFE and SE mechanisms, the relation between IR and VR is expressed as follows, respectively [7, 24]:

$$I_{R} = I_{o} \exp \left( {\frac{{\beta_{PF} V^{0.5} }}{{kTd^{0.5} }}} \right)$$
(5a)
$$I_{R} = I_{o} \exp \left( {\frac{{\beta_{SC} V^{0.5} }}{{kTd^{0.5} }}} \right)$$
(5b)

In Eq. 5a and 5b, d is the interfacial layer thickness, βPF and βSC are PFE and SE coefficients and theoretical value of them is given as follows [7]:

$$2\beta_{SC} = \beta_{PF} = \left( {\frac{{q^{2} }}{{\pi \varepsilon_{0} \varepsilon_{i} }}} \right)^{0.5}$$
(5c)

Here εi and εo (8.85 × 10−12 F/m) are the dielectric of interlayer and vacuum, respectively. The theoretical βPF and βSC values are calculated as 3.89 × 10−5 eV−1m0.5V0.5 and 3.73 × 10−5 m0.5V0.5, respectively. As seen in Fig. 6, the ln(IR)–V 0.5R plot shows good linear behavior for these two structures. The experimental value of β was obtained from the slope of these plots as 1.46 × 10−5 eV−1m0.5V0.5 for MS and 3.12 × 10−5 m0.5V0.5 for MPS structures, respectively. These theoretical and experimental values of β show that the CCM is dominated by SE in the MS structure, whereas PFE is dominated in MPS structure due to the current conduction is composed of the metal into conductive dislocations via surface states or traps [7].

In order to determine whether or not the passivated (Fe2O4-PVP) interfacial organic layer effect Nss, the energy-dependent of the Nss was obtained from the IF–VF plots by using following Eq. 6a, 6b for MS and MPS structure by considering V dependent BH and n were given in Fig. 7. The energy-dependent profile of the Nss can be obtained from Eq. 2 as follows [7, 8].

Fig. 7
figure 7

Nss–(Ec–Ess) of the MS and MPS structures

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$$N_{ss} \left( V \right) = \frac{1}{q}\left[ {\frac{{\varepsilon_{i} }}{{d_{i} }}\left( {n\left( V \right) - 1} \right) - \frac{{\varepsilon_{s} }}{{W_{D} }}} \right]$$
(6a)

Here, the depletion layer width acquired from the C−2–V plots at reverse biases is denoted by WD. The values of Nss with respect to the bottom of conductance band (Ec) are expressed as follows.

$$E_{c} - E_{ss} = q\left( {\varPhi_{e} - V} \right)$$
(6b)

Here, Φe [(1–n−1)V] is the effective BH. In Fig. 7, the increment of Nss values from the mid-gap of Si towards bottom edge of Ec were almost seen as exponentially. MPS structure’s Nss values are also substantially low when compared with MS structure in the whole energy range.

These results are validated that the (Fe2O4-doped PVP) organic interlayer enhanced the performance of MS because of incorporation in PVP lattices reduces many oxygen vacancies and leads to lower density of charge carriers, which can also effectively increase the BH [3, 16, 27,28,29,30,31,32,33,34]. These mean values of Nss (~ 1013 eV−1 cm−2) are suitable for these structures.

3.2 Forward and reverse bias C–V and G/ω–V Characteristics

The other electrical parameters such as the density of donor atoms (ND), Fermi energy (EF), ΦB(C–V), WD, maximum electric field (Em), Rs, and Nss were obtained from the C–V and G/ω–V characteristics (Figs. 8 and 9) for 1 MHz. As shown in these curves, these plots have three regimes which are accumulations, depletions, and inversions like MIS structure.

Fig. 8
figure 8

C–V plots of the MS and MPS structures

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Fig. 9
figure 9

G/ω–V plots of the MS and MPS structures

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The C−2–V plots of the MS structures with Fe2O4-doped PVPAu/n-Si interlayer and without interlayer were given in Fig. 10. These plots have a well linear zone in wide biases interval for two structures.

Fig. 10
figure 10

C−2–V plots of the MS and MPS structures

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The values of ND, EF, ΦB(C–V), WD, and Em were calculated from the slopes and intercepts at Fig. 10 as 9.08 × 1014 cm−3, 0.258 eV, 0.914 eV, 9.53 × 10−5 cm, and 1.32 × 104 V/cm for MS and 7.65 × 1014 cm−3, 0.263 eV, 0.981 eV, 1.29 × 10−4 cm, and 1.27 × 104 V/cm for MPS structure by using following equations [6, 7]:

$$\left[ {N_{D} = 2/q_{so} A^{2} \left( {\frac{{dC^{ - 2} }}{dV}} \right)} \right]$$
(7a)
$$E_{F} = \frac{kT}{q}{ \ln }\left( {\frac{{N_{C} }}{{N_{D} }}} \right)$$
(7b)
$${\text{E}}_{\text{m}} = \left[ {\left( {2{\text{qN}}_{{\text{D}}} {{\text{V}}}_{\text{o}} } \right)/(\varepsilon_{\text{s}} \varepsilon_{\text{o}} )} \right]^{1/2}$$
(8a)
$$W_{D} = \left( {{{2\varepsilon_{s} V_{D} } \mathord{\left/ {\vphantom {{2\varepsilon_{s} V_{D} } {qN_{D} }}} \right. \kern-0pt} {qN_{D} }}} \right)^{1/2}$$
(8b)

Hence, the ΦB(C–V) value can be derived from the following equation [7].

$$_{B} \left( {C - V} \right) = V_{o} + \frac{kT}{q} + E_{F}$$
(9)

In Eqs. 7 and 8; the quantities of εs, NC (= 2.8 × 1019 cm−3), VD are the dielectric permittivity of Si (11.8), the density of states in the Ec, and diffusion potential (= Vo + kT/q) [7], respectively. The obtained BH from the IF–VF characteristics is lower than at about EF energy obtained from the CR–VR data for 1 MHz for two type structures due to the result of voltage, measurement method and barrier in-homogeneities, because the apparent BH from the M to S is lower than the S to M for charge carriers. Additionally, under forward bias, current follows the line through lower BHs since the barrier is inhomogeneous and so leads to increase in current or decrease in ΦBo. So, that BH is certainly the nominal arithmetic mean of these patches [27].

The value of Rs arise from many reasons such as the back and front contacts formation, bulk resistivity, impurities or dislocations, probe wires and in-homogeneity of doping atoms and interlayer and it is more effective on the C–V and G/ω–V measurements at high frequencies at accumulation region [35,36,37,38,39]. Thus, the voltage dependent Ri of these two structures for 1 MHz were also obtained using equation below presented by Nicollian and Brews and indicated in Fig. 11 [9]:

Fig. 11
figure 11

Ri–V plots of the MS and MPS structures

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

In Eq. 10; the measured G and C values for biases are Gm and Cm. But, the real value of Rs corresponds to Ri value at strong accumulation region for a MIS or MOS structure. Thus, the real value of Rs was calculated from Eq. 10 as 168 Ω and 126 Ω for MS and MPS structures at 3 V, respectively. Similar results have been reported by various researchers [40,41,42].

4 Conclusions

In the present study, Au/n-Si structures with and without Fe2O4-doped PVP interlayer were investigated at same conditions to determine the effects of (Fe2O4-doped PVP) organic interfacial layer on the I–V, C–V and G–V characteristics as well as performance of the MS structure at room temperature. For these purposes, both the I–V and C/G–V (at 1 MHz) measurements were performed at room temperature. In this way, the values of n, BH and Rs were obtained using the different experimental measurement methods and also calculated methods namely TE theory, Cheung’s and Nicollian-Brews methods and compared with each other. When these experimental results are compared for MS and MPS structures, it is seen that the used (Fe2O4-doped PVP) interlayer at M/S interface leads to a quite decreases in Rs, Nss, leakage current and an increase in rectifying rate (RR), Rsh and BH. The obtained BH from the forward bias I–V data was found lower than its obtained values from the CR–VR data for 1 MHz for two type structures and it is attributed to the voltage and measurement method, because the apparent BH from the M to S is lower than the semiconductor to metal for charge carriers. In conclusion, the interfacial organic layer (Fe2O4-doped PVP) significantly improves the performance of the MS structure and so it can be successfully used instead of traditional insulator layer from the point of easy growth processes with lower cost and energy consumption, low weight per molecule and flexibility.