1 Introduction

Metal–semiconductor (MS) junctions play an important role in the construction of electronic appliances because of their specific features, low voltage drop, fast switching, low tenancy space in integrated electronics, and minimal cost; additionally, MSs are utilized as Schottky barrier diodes in OLEDs, photovoltaic cells, OFETs, thermistors, switching and memory systems, organic solar cells and negative–resistance devices [1,2,3,4]. To fabricate these devices, indium phosphide (InP) is an exquisite semiconductor substance owing to its distinctive physical and electrical properties. Conversely, it is difficult to reach a barrier height greater than 0.5 eV on an InP substrate because the surface Fermi level pinning increases as the occurrence of enormous surface states and different nonstoichiometric defects increases [5]. Thus, a high reverse leakage current is achieved due to the low barrier height of InP-based Schottky diodes, which results in poor electrical performance in the devices. To overcome this issue there may be several techniques available to modify and continuously manipulate the barrier height wherein organic/polymer interlayers are used between the metal and semiconductor [6,7,8,9,10]. The fabrication and characterization of MS junctions with organic/polymer interlayers are challenging issues in the research/scientific community.

Recently, the size of electronic devices has reached the molecular entity scale, as confirmed by the increasing attention given to the considerate transport of organic molecules associated with two metal contacts [11] and metal/organic or polymer MS junctions [6]. It is widely accepted that the interfacial layer (IL) established at the metal–semiconductor interface organizes the electrical features of Schottky contacts. As a result, the evaluated barrier properties of the metal/IL/semiconductor contacts are better than those of traditional MS junctions, which may be attributed to the space-charge region of the semiconductor. Numerous investigations have shown that the barrier heights of MS junctions can be improved by the addition of organic or polymeric layers in the middle of metals and semiconductors [12,13,14,15,16,17,18,19,20,21,22,23,24].

Organic materials have attracted extensive attention for their use in molecular electronic and optoelectronic devices [13, 25]. In recent years, phthalocyanines created from organic materials have played a vital role in the manufacture of devices with organic molecules. Notably, cobalt phthalocyanine (CoPc) has semiconducting properties and is a metal phthalocyanine (MPc) that can be regularly employed in several organic electronic devices [26]. Furthermore, metal phthalocyanines are water and air-stable, thermally strong and harmless, and may be sublimed or sputtered with highly even films on different substrates. Metal phthalocyanines are also quite cheap and easy to prepare. In particular, CoPc can be used as a hole-injection layer, with considerable upgrades in turn-on voltage and luminance in OLEDs. Additionally, Kao et al. [27] confirmed the enhancement in the turn-on voltage and luminance in OLEDs with the use of the CoPc layer as a hole injection layer. CoPc may also be utilized to fabricate carbon-black-based electrocatalysts. Other advantages of organic materials over insulators or oxide materials include easy preparation, low cost and power ingesting, low weight, great mechanical stability, water-solubility and good charge storage capacity. Furthermore, the CoPc films on the InP substrate offer numerous advantages, including enhanced spin manipulation, improved photovoltaic performance, enhanced optoelectronic properties, versatile integration in multifunctional devices, and tunable magnetic sensitivity. Considering these notable characteristics of an organic interlayer (CoPc), in this work, Au/CoPc/un-InP metal/polymer/ semiconductor (MPS)-type Schottky diodes were prepared with a cobalt phthalocyanine interlayer. The overall performance and operating range of these junctions are associated with many issues including surface preparation, barrier height homogeneity and interlayer at the interface, surface state density (NSS), shunt (Rsh) and series resistance (RS), and applied bias potential, frequency and temperature [13, 16, 24]. Mainly, the interfacial layer, NSS, RSh, RS and applied electric field/voltage are extra active in the performance of the junction. Current–voltage (I-V) measurements of the Au/CoPc/un-InP MPS diodes were performed and the barrier height, RSh, RS and NSS were determined at room temperature. These derived parameters are correlated with the results of the Au/un-InP Schottky diode (SD) to assess the influence of the interlayer at the interface. Similarly, the conceivable forward and reverse leakage transport processes of the Au/un-InP and Au/CoPc/un-InP MPS diodes are depicted and described.

2 Experimental Procedure

First, one side of a polished undoped-InP (un-InP) wafer (bought from Semiconductor Wafer, Inc., Taiwan) was cut into slices, after which the slices were gutted with warm organic solvents to eliminate impurities by ultrasonication for 5 min every step. Later, to remove the native oxide on the InP surface, the wafer was washed with dilute aqua regia 2HNO3:2HCl:1H2O for 3 min and dipped in DI water followed by drying with nitrogen gas. Then, the indium (In) was coated on the unpolished side of the wafer as an ohmic contact, subsequently, the contacts were annealed at 350 °C for 1 min under ambient nitrogen. Then, cobalt phthalocyanine (CoPc) films were coated on the InP surface under a vacuum of 7 ~ 8 × 10–6 mbar using a thermal evaporation approach. The CoPc film thickness was approximately 40 nm which was measured by a profilometer. Afterwards, gold (Au) Schottky junctions were prepared by an e-beam evaporation method with a 0.7 mm diameter on a CoPc film. The developed configuration was an Au/CoPc/un-InP metal/polymer/semiconductor (MPS) type Schottky diode. Furthermore, an Au/un-InP Schottky diode (SD) was prepared without the CoPc layer for comparison with the results of the MPS junction. The chemical states, structural and morphological properties of the CoPc/InP layers were studied using XPS, Raman and atomic force microscopy (AFM) measurements. The SD and MPS diodes were electrically measured through the current–voltage (I-V) approach by a Keithley 2400 source measuring unit.

3 Results and Discussion

The structural properties of CoPc films on quartz glass were analysed using Raman measurements. The Raman spectrum as shown in Fig. 1 was measured using an argon laser at an excitation wavelength of 488 nm in the range from 500 to 1700 cm−1. The characteristic vibrational bands identified at 593 and 682 cm−1 correspond to C-N bond stretching (A1g bond) due to benzene ring formation and C–C vibration, respectively, in the CoPc molecule [28, 29]. The vibrational band with the maximum intensity is observed at 1537 cm−1 and is correlated with the B1g mode and corresponds to the stretching of the C = N  bond. The vibrational band observed at 1537 cm−1 signifies the crystalline quality of the CoPc compound [30].

Fig. 1
figure 1

Raman measurements of the CoPc films on a glass plate

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The XPS survey spectrum of CoPc depicted in Fig. 2a, shows the presence of four elements: C 1s, N 1 s, O 1s, and Co 2p, with the oxygen originating from the oxygen-containing groups within CoPc. The remaining elements are consistent with the elemental composition of CoPc. Figure 2b shows that the high-resolution C 1s spectra exhibited four peaks located at binding energies (BE) of 284 eV, 285.35 eV, 286.15 eV, and 287.25 eV, which are attributed to (C − C), (C = C), (C − O/C − N) and (C = O/C = N), respectively [31,32,33,34,35,36,37]. The N 1s spectrum presented in Fig. 2c clearly shows four kinds of nitrogen. Specifically, the peaks located at BEs of 398.52 eV and 400.05 eV correspond to nitrogen atoms within the phthalocyanine ring, while the peak at a BE of 400.5 eV indicates the presence of an amide (− O = C − NH), confirming the success of the reaction between phthalocyanine and critic acid. Additionally, the peak at a BE of 398.81 eV is ascribed to the coordination between cobalt and nitrogen [31, 35, 36]. Figure 2d shows the Co 2p spectra, two peaks are observed at BEs of 780.64 eV (its satellite peak at 782.7 eV) and 796.15 eV which are assigned to Co 2p3/2 and Co 2p1/2, respectively [38]. Figure 2e illustrates the In 3d spectrum, where the 3d3/2 and 3d1/2 peaks are detected at BEs of 444.84 and 452.49 eV, respectively [39]. Figure 2f presents the high-resolution P 2p spectrum, which includes contributions. In particular, the 2p1/2 and 2p3/2 peaks are observed at BEs of 132.18 eV and 128.51 eV, respectively, indicating the presence of the phosphide (P−3) [39, 40]. The results confirm that the CoPc is formed on the InP surface.

Fig. 2
figure 2

XPS spectra of the CoPc/InP interface: (a) survey spectra of CoPc, (b) C 1 s, (c) N 1 s, (d) Co 2P, (e) In 3d, and (f) P 2p

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To assess the influence of the CoPc interlayer on the electronic features of the Au/undoped InP Schottky diode (SD), a Au/CoPc/un-InP metal/polymer/semiconductor (MPS)-type Schottky diode was fabricated and the outline sketch is shown in Fig. 3a. Figure 3b depicts the AFM topography of the thermally deposited CoPc films on the un-InP surface measured in the active area of 2 μm × 2 μm. The acquired RMS of the CoPc film is 4.499 nm, which suggests that the morphology of the CoPc film surface is noticeably smooth. Figure 4 depicts the I-V features of the Au/un-InP Schottky diode and Au/CoPc/un-InP MPS diode. A higher rectification ratio is obtained for the MPS diode (327) than for the SD (10) diode at a bias of 3 V. The nonsaturation behavior of the I-V curves is perceived for both the SD and MPS diodes, which might be credited to generation-recombination, image force reduction and the existence of an interface layer [18, 41]. A reduced leakage current in the reverse bias is observed for the MPS diode (1.835 × 10–7 A at -1 V) compared to the SD (1.335 × 10−5A at -1 V) which suggests that the electrical assets are enriched after the insertion of CoPc as an interlayer between the Au and un-InP semiconductor. The barrier height (ΦB) and ideality factor (n) of the SD and MPS diodes are acquired based on the TE model [42]. The derived magnitudes of ΦB and n of the SD and MPS diode are 0.66 eV and 1.58, and 0.77 eV and 1.42, respectively. The results showed that ΦB was more enhanced for the MPS diode than for the SD, indicating that the CoPc interlayer modifies ΦB by altering the space charge at the CoPc-InP junction [13]. Thus, the CoPc film forms a real barrier that blocks the direct interface between the Au and the InP surface. Additionally, the CoPc interlayer drastically altered the InP's electron affinity and the metal's work function [13, 43]. A similar observation indicated that the increase in ΦB of the MPS diode can allow the substrate band bend through the interlayer [9]. Our investigational findings indicate that the magnitude of deviation of ideality factor from unity for the SD and MPS diodes may be due to the existence of an excess current, a possible decrease in potential across the interfacial layer, and the incidence of series resistance and recombination current over the interface states at the junction [44]. Other reasons may include the inhomogeneous interface, uneven charge distribution at the interface, MIGS and voltage-dependent ΦB at the interface [45, 46]. One more prospect may be due to the occurrence of secondary mechanisms inclusive of interface dipoles initiated via polymer interlayers or certain interface configurations, and to manufacture-caused flaws at the junction [47].

Fig. 3
figure 3

(a) Outline of the Au/CoPc/un-InP MPS diode with a CoPc interlayer and (b) AFM image of the CoPc film on the un-InP surface

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Fig. 4
figure 4

Current–voltage (I-V) plot of the Au/un-InP SD and Au/CoPc/un-InP MPS diodes

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The performance and steadfastness of electronic devices depend strongly on the series resistance (RS) and shunt resistance (RSh). Hence, it is imperative to evaluate the RS and RSh of the SD and MPS diodes. Figure 5 elucidates the variation in Rj, and the junction resistance with V for the SD and MPS diodes, from which the RS and RSh are estimated. Mainly, a low RS directs enhanced current transport across the junction, whereas a magnitude of RSh close to the edge indicates an insignificant leakage current across the junction. The magnitudes of RS and RSh are determined from the plot (Fig. 5), in which, the lower part gives the RS in the forward bias, while the maximum peak provides the RSh in the reverse bias. The RS and RSh values are predicted to be 3.2 kΩ and 120.7 kΩ for the SD and 9.8 kΩ and 34.1 MΩ for the MPS diode, respectively.

Fig. 5
figure 5

Plot of junction resistance (Rj) versus voltage (V) for the Au/un-InP SD and Au/CoPc/un-InP MPS diodes

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It is noted that in the higher current section of the forward bias, the I-V curves deviate which is probably due to the RS, density of states and presence of the interfacial layer. Thus, ΦB, n and RS are predicted in the higher current part of the I-V curves of the SD and MPS by using the method suggested by Cheung's [48] functions. Figure 6a and b illustrate the variations between dV/d(lnI) and I and between H(I) and I for the SD and MPS diodes. The slope and y-axis intercept of the \({\text{dV}}/{\text{d}}\left({\text{lnI}}\right)-{\text{I}}\) plot (Fig. 6a and b) represent the RS and n, and the analogous values are 1.67 kΩ and 1.79, and 3.54 MΩ and 3.13 for the SD and MPS, respectively. The slope and y-axis intercept of the  \(\mathrm {H}\left({\text{I}}\right)-{\text{I}}\) plot (Fig. 6a and b) represent the RS and ΦB, respectively, and the analogous values are 1.60 kΩ and 0.69 eV, and 3.49 MΩ and 0.73 eV for the SD and MPS diodes, respectively. The results indicate that the predicted RS values from Cheung’s plots are well matched, which indicates that Cheung's derivations are trustworthy and expedient. ΦB is closely matched with the value derived by way of the forward bias \({\text{ln}}\left({\text{I}}\right)-{\text{V}}\) plot. In contrast, the n estimated using the \({\text{dV}}/{\text{d}}\left({\text{lnI}}\right)-{\text{I}}\) plot differs to some extent from the value determined by the forward-bias \({\text{ln}}\left({\text{I}}\right)-{\text{V}}\) plot. This might be because the RS and interface properties affect the I-V curves, but the RS affects only the \({\text{dV}}/{\text{d}}\left({\text{lnI}}\right)-{\text{I}}\) plot [49, 50]. The modified Norde method [51] was also applied to obtain the ΦB and RS for the SD and MPS diodes. Figure 7 shows the Norde graph for the SD and MPS diodes, wherein, ΦB and RS are assessed. The predicted ΦB and RS values are 0.64 eV and 22 kΩ, 0.78 eV and 1.8 MΩ for the SD and MPS diodes, respectively. The findings reveal that the ΦB values are similar to the values obtained with the aid of the I-V technique.

Fig. 6
figure 6

Plot dV/d(lnI) versus I, and H(I) versus I for the (a) Au/un-InP SD and (b) Au/CoPc/un-InP MPS diodes

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Fig. 7
figure 7

Norde plot (F(V)-V) of the Au/un-InP SD and Au/CoPc/un-InP MPS diodes

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Werner proposed a simple method [52] to calculate the barrier parameters (RS and n) from forward bias current–voltage characteristics of the contacts. Under forward bias conditions, the forward voltage (V-IRS) is much greater than nkT/q, and the differential conductance (G) is defined as G = dI/dV. The diode current, based on the thermionic mechanism, can be expressed as

$$I={I}_{S}exp\left(\frac{\beta }{n}\left(V-I{R}_{S}\right)\right)$$
(1)

The above equation yields the small signal conductance \(G=\frac{dI}{dV},\)

$$\frac{G}{I}=\frac{\beta }{n}\left(1-G{R}_{S}\right)$$
(2)

Further, a plot between G/I versus G can be used to analyze the device characteristics. Using Eq. (2), the plot of G/I versus G (shown in Fig. 8a and b) for the SD and MPS diodes yields a straight line that leads to the evaluation of 1/RS and β/n from the x- and y-axis intercept, respectively. The straight line observed in Fig. 8a and b indicates the well-defined interfaces and good quality of the devices. Moreover, Werner's approach is effective in the voltage region where the effect of series resistance on the current is important. The determined RS and n values are 1.47 kΩ and 2.04, and 1.22 MΩ and 3.77 for the SD and MPS diodes. These parameters were comparable to those evaluated by Cheung and Norde methods.

Fig. 8
figure 8

Plot of G/I versus G for the (a) Au/un-InP SD and (b) Au/CoPc/un-InP MPS diodes

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Considering the existence of an oxide layer on the semiconductor surface, the current generated via the MS junction may be stated by [42].

$${\text{I}}={{\text{AA}}}^{*}{{\text{T}}}^{2}{\text{exp}}\left(-\frac{{\text{q}}{\Psi }_{{\text{S}}}}{{\text{kT}}}\right)\left[-\frac{{{\text{qV}}}_{{\text{p}}}}{{\text{nkT}}}\right]$$
(3)

Here A*, T, A, k, and n are typically defined as follows [18]. The critical surface potential \({\Psi }_{{\text{S}}}\left({{\text{I}}}_{{\text{C}}},{\mathrm{ V}}_{{\text{C}}}\right)\) and the critical voltage Vc are empirically identified, and the BH may be acquired. ΨS is the surface potential and is defined as [53].

$${\Psi }_{{\text{S}}}=\frac{{\text{kT}}}{{\text{q}}}{\text{ln}}\left[\frac{{{\text{AA}}}^{*}{{\text{T}}}^{2}}{{\text{I}}}\right]-{{\text{V}}}_{{\text{p}}}$$
(4)

ΨS is determined by using the value of Vp, and the Vp value is obtained using \({{\text{V}}}_{{\text{p}}}=\frac{{\text{kT}}}{{\text{q}}}{\text{ln}}\left({{\text{N}}}_{{\text{v}}}/{{\text{N}}}_{{\text{a}}}\right)\); now Nv and Na usually have meanings [18]. The acquired Ψs values are contrary to the forward bias voltages for the SD and MPS diodes and are illustrated in Fig. 9. The critical surface potential \({\Psi }_{{\text{S}}}\left({{\text{I}}}_{{\text{c}}},{\mathrm{ V}}_{{\text{c}}}\right)\) and the critical voltage Vc are derived from the ΨS-V plot, so ΦB is derived. Figure 9 demonstrates that the ΨS value decreases linearly until V reaches the critical value Vc. The BH is defined as

Fig. 9
figure 9

Plot of ΨS versus forward-bias voltage for the Au/un-InP SD and Au/CoPc/un-InP MPS diodes

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$${\Phi }_{{\text{B}}}={\Psi }_{{\text{S}}}\left({{\text{I}}}_{{\text{c}}},{{\text{V}}}_{{\text{c}}}\right)+\mathrm{\alpha }{{\text{V}}}_{{\text{c}}}+{{\text{V}}}_{{\text{p}}}$$
(5)

Furthermore, quantity α is the converse of the ideality factor (n) and is defined as

$$-\mathrm{\alpha }=\frac{1}{{\text{n}}}={\left(\frac{{\text{d}}{\Psi }_{{\text{S}}}}{{\text{dV}}}\right)}_{{{\text{I}}}_{{\text{C}}},{{\text{V}}}_{{\text{C}}}}$$
(6)

The ΦB and n values are derived by Eqs. (5) and (6) for the SD and MPS diodes and the respective magnitudes are 0.64 eV and 2.84, and 0.77 eV and 1.98, respectively. The ΦB magnitudes acquired from the forward-bias I-V data, Cheung’s plots and Ψs-V curves are nearly the same, which suggests that the approaches employed here are consistent and reliable.

The density of states (NSS) of the Au/un-InP SD and Au/CoPc/un-InP MPS diode is acquired from the forward bias I-V data based on \({\text{n}}\left({\text{V}}\right)\) and Φe. The NSS is defined as [54]

$${{\text{N}}}_{{\text{SS}}}=\frac{1}{{\text{q}}}\left[\frac{{\upvarepsilon }_{{\text{i}}}}{{\text{q}}}\left({\text{n}}\left({\text{V}}\right)-1\right)-\frac{{\upepsilon }_{{\text{S}}}}{{{\text{W}}}_{{\text{D}}}}\right]$$
(7)

Here Wd, εs,εi, δ and \({\text{n}}\left({\text{V}}\right)\) are usually defined [18], and nV can be defined as \({\text{n}}\left({\text{V}}\right)=\left({\text{q}}/{\text{kT}}\right)\left[{\text{V}}/\left({\text{ln}}\left({\text{I}}/{{\text{I}}}_{{\text{o}}}\right)\right)\right]\). In an n-type semiconductor, the energy of interface states (ESS) concerning the lowest of the conduction band at the surface of the semiconductor is stated by

$${{\text{E}}}_{{\text{C}}}-{{\text{E}}}_{{\text{SS}}}=\mathrm{q }\left({\Phi }_{{\text{e}}}-{\text{V}}\right)$$
(8)

Φe is defined by

$${\Phi }_{{\text{e}}}={\Phi }_{{\text{b}}}+\mathrm{\beta V},\mathrm{ \ where } \ \frac{{\text{d}}{\Phi }_{{\text{e}}}}{{\text{dV}}}=\upbeta =1-\frac{1}{{\text{n}}\left({\text{v}}\right)}$$
(9)

Figure 10 shows the variation in the NSS with \({{\text{E}}}_{{\text{C}}}-{{\text{E}}}_{{\text{SS}}}\) for the SD and MPS diodes, wherein, the NSS magnitudes (Fig. 10) decrease with increasing \({{\text{E}}}_{{\text{C}}}-{{\text{E}}}_{{\text{SS}}}\). The derived NSS magnitudes are in the range of 7.12 × 1012 eV−1 cm−2 to 3.91 × 1011 eV−1 cm−2 for the SD and 4.42 × 109 eV−1 cm−2 to 2.19 × 1010 eV−1 cm−2 for the MPS diodes. The NSS magnitude acquired for the MPS diode is less than the value acquired for the SD, implying that the InP surface is effectively passivated by the CoPc layer and, consequently the lower NSS. The findings indicated that the CoPc interlayer results in tremendous adjustments in the interfacial states, although the polymer/un-InP interface appears to be abrupt and unreactive [15, 16]. The results suggest that the CoPc layer plays a generous role in decreasing NSS and enriching the Φe of the SD. The determined ΦB, n, RS and NSS values of the SD and MPS diodes are summarized in Table 1.

Fig. 10
figure 10

NSS versus EC – ESS plot for the Au/un-InP SD and Au/CoPc/un-InP MPS diodes

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Table 1 The calculated various electronic parameters of the Au/un-InP SD and Au/CoPc/un-InP MPS
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The thermionic emission mechanism is applied in a Schottky contact to model the current–voltage properties in the evaluation of barrier parameters such as barrier height and ideality factor for forward voltage V < 3kT/q. On the other hand, the log I vs. log V graph of the diodes provides insight into the conduction properties that are directly related to the space charges present at the junction. These properties depend greatly on the mobility of the carriers, bias potential, and traps that are present at the junction [55, 56]. To explore the forward current conduction processes in the SD and MPS diodes, log I versus log V are plotted and illustrated in Fig. 11, where three different linear regions are noted (labeled as part-I, part-II and part-III) and every slope has its value that follows the \(\mathrm{I\alpha }{{\text{V}}}^{{\text{m}}}\) relation (here, m is the power exponent, and the slope of the linear section of each part provides the m value, i.e., the current is proportionate to the applied bias). For the SD and MPS diodes, the m values are estimated to be 1.00, 3.57, 1.13 and 1.11, 5.54, 2.78 in parts I, II and III, respectively. Seemingly, in the lower-bias section (part-I), the current conduction shows ohmic properties for both the SD and MPS diodes. The value of 'm' close to 1 indicates a possible linear relationship between voltage and current due to thermally generated carriers [57,58,59]. The I-V correlation may be described by way of the power law dependence. In part-II, the slope values are greater than 2 for both the SD and MPS diodes, which could be inferred as a trap-charge limiting current process (TCLC) with traps distributed exponentially [18, 23, 60]. Thus, an increased density of injected electrons leads to the filling of traps and the escalation of space charges [23, 61]. Additionally, the slope values of the SD and MPS diode gradients decrease in the upper-bias section (part-III) as junctions reach the trap-filled limit. As a result, electrons escape the trap because of the sturdy injection of electrons and give rise to the SCLC. The findings exhibit a coherent transformation from an ohmic-type conduction at the lower-bias section (part-I) to an SCLC at the upper-bias section (part-II and part-III) for both the SD and MPS diodes. However, the thermionic emission currents and space charge limited emission currents are always competing transport processes in Schottky contacts.

Fig. 11
figure 11

Plot of log(I) versus log(V) for the Au/un-InP SD and Au/CoPc/un-InP MPS diodes

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To analyze the reverse current transport mechanisms in the SD and MPS diodes, Fowler–Nordheim (FN), Poole–Frenkel emission (PFE) and Schottky emission (SE) are considered via the interface. However, numerous conduction processes might also arise at specific applied voltages. As a result, it is challenging to comprehend entirely and assess the reliable current transport process for the FN, PFE and SE. The current is ruled by the FN across the junction and is defined as [18, 62,63,64].

$${{\text{I}}}_{{\text{FN}}}={{\text{AV}}}^{2}\mathrm{ exp}\left(-\frac{{\text{B}}}{{\text{V}}}\right),\mathrm{ where \ A}=\frac{{{\text{q}}}^{3}{\text{m}}}{8\uppi {{\text{m}}}^{*}{\Phi }_{{\text{b}}}},\mathrm{ B}=8\uppi {\left({\text{q}}{\Phi }_{{\text{b}}}\right)}^{3}/3{\text{qh}}$$
(10)

Here q, h and m* are common denotations [18]. The plot of ln(I/V2) versus 1/V for the SD and MPS diodes is depicted in Fig. 12a. The plot reveals a linear curve with a positive slope. As stated by Eq. (10), the slope must be negative; and consequently, the impact of FN tunneling is probably a constrained conduction process in both the SD and MPS diodes. The reverse current is governed by the PFE and is described by [63, 64].

$${{\text{I}}}_{{\text{R}}}={{\text{I}}}_{{\text{o}}}{\text{exp}}\left(\frac{{\upbeta }_{{\text{PF}}}{{\text{V}}}^{1/2}}{{{\text{kTd}}}^{1/2}}\right)$$
(11)

and for the SE

Fig. 12
figure 12

(a) Plot of (a) ln(I/V2) versus 1/V and (b) Plot of ln(IR) versus V1/2 for the Au/un-InP SD and Au/CoPc/un-InP MPS diodes

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$${{\text{I}}}_{{\text{R}}}={{\text{AA}}}^{* }{{\text{T}}}^{2 }{\text{exp}}\left(-\frac{{\Phi }_{{\text{S}}}}{{\text{kT}}}\right){\text{exp}}\left(\frac{{\upbeta }_{{\text{SC}}}{{\text{V}}}^{1/2}}{{{\text{kTd}}}^{1/2}}\right)$$
(12)

Here d is the depletion width, βPF is the PFE and βSC is the SE lowering constant. The hypothetical values for βPF and βSC are given by

$${2\upbeta }_{{\text{SC}}}={\upbeta }_{{\text{PF}}}={\left(\frac{{{\text{q}}}^{3}}{\uppi {\upvarepsilon }_{{\text{o}}}{\upvarepsilon }_{{\text{r}}}}\right)}^{1/2}$$
(13)

Using Eq. (13), the hypothetical values for βPF and βSC are acquired, the values are 2.15 × 10–5 \({\text{eV}}{\mathrm{ m}}^{1/2}{{\text{V}}}^{-1/2}\) and 1.07 × 10–5 \(\mathrm{eV }{{\text{m}}}^{1/2 }{{\text{V}}}^{-1/2}\) for the SD, and 4.05 × 10–5 \({\text{eV}}{\mathrm{ m}}^{1/2 }{{\text{V}}}^{-1/2}\) and 2.02 × 10–5 \(\mathrm{eV }{{\text{m}}}^{1/2 }{{\text{V}}}^{-1/2}\) for the MPS diode, respectively. A ln (IR) versus VR1/2 graph plotted for the SD and MPS diodes is presented in Fig. 12b. As shown in Fig. 12b, there are two different straight regions (labeled as part-I and part-II) for the SD and MPS diodes, where the observed magnitudes of the slopes are 2.88 × 10–5 \({\text{eV}}{\mathrm{ m}}^{1/2 }{{\text{V}}}^{-1/2}\) and 1.26 × 10–5 \(\mathrm{eV }{{\text{m}}}^{1/2 }{{\text{V}}}^{-1/2}\) for the SD and 5.58 × 10–5 \({\text{eV}}{\mathrm{ m}}^{1/2 }{{\text{V}}}^{-1/2}\) and 1.41 × 10–5 \(\mathrm{eV }{{\text{m}}}^{1/2 }{{\text{V}}}^{-1/2}\) for the MPS diode in part-I and part-II, respectively. In part-I, the slope magnitudes are well coordinated with the hypothetical magnitudes of βPF; hence, PFE is dominant in the reverse leakage current in the lower–bias section for both the SD and MPS diodes. Although the slope values in part-II nearly concur with the hypothetical values of βSC, the SE has ruled the reverse leakage current in the higher-bias section for both the SD and MPS diodes. Due to the nonuniformity and subatomic structure of the CoPc layer, reverse current conduction occurs over the contact interface in the SE instead of from the bulk material [18, 65]. In the case of PFE, the occurrence of a large density of structural defects or trap levels in the CoPc film can account for the increased concert of trapped/detrapped charge carriers [14, 18]. Figure 13 shows the energy band diagrams of the CoPc/InP structure before contact, after contact, and under dark conditions.

Fig. 13
figure 13

Schematic energy band diagrams of the CoPc/InP structure (a) before contact, (b) after contact, and (c) under dark conditions

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4 Conclusions

In this work, first, cobalt phthalocyanine (CoPc) films were thermally deposited on an un-InP substrate and their chemical, structural and morphological properties were probed via XPS, Raman and AFM approaches. Raman measurements of the phthalocyanine thin films revealed dominant characteristic vibrational bands at 1537 cm−1, indicating the crystalline quality of the films. XPS results confirmed that the CoPc film was formed on the un-InP surface. Then, the Au/CoPc/un-InP MPS diode and Au/un-InP SD were fabricated, and their electrical properties were examined via the I-V technique. The derived barrier heights (ΦB) were 0.66 eV and 0.77 eV for the SD and MPS diodes, respectively. An increase in ΦB was observed for MPS compared with SD, implying that ΦB was modified by using a thin CoPc interlayer. The BHs were also derived through Cheung's, and Norde methods, and the Ψs-V curves are almost equal to the values derived from the I-V data, which indicates that the methods implemented here are trustworthy and effective. The Rs of the SD and MPS diodes were derived by the I-V, Cheung, and Norde methods and the corresponding magnitudes are analogous. The results confirmed that the expected NSS was lower for the MPS diode than for the SD, suggesting that the CoPc layer plays a generous role in decreasing the NSS. For the SD and MPS, the forward current conduction process was ruled out by the ohmic nature and SCLC in the lower-bias and higher-bias sections. The reverse leakage current is directed by the PFE in the lower–bias section, while, the SE is governed in the higher-bias section for both the SD and MPS diodes. The results revealed that the CoPc layer is a potential material for the development of organic–inorganic electronic devices.