1 Introduction

The metal–insulator-semiconductor (MIS) structure is used as a basic component in various electronic and optoelectronic device applications such as MIS diode, MIS solar cell, MIS capacitor, and MIS field effect transistor (FET) [1,2,3]. The MIS diode, also called as Sohottky barrier diode, consists of an insulator material separating the doped semiconductor and the metal top contact called rectifier. Moreover, the MIS diode has a metal back contact called ohmic [1,2,3,4,5,6,7]. This insulator, which has dielectric property, blocks any dc current. Therefore, MIS diode has zero dc current. Besides, the MIS diode because of the existence of the insulator have advantages such as higher rectification ratio and lower leakage current. The interfacial insulator layer has a significant effect on the magnitude of the current flowing through the diode. Electrical performance and characteristics of MIS diode depend on the homogeneity of the insulating layer, interface states (Nss), and series resistance (Rs).

In MIS diode, current or charge carrier transport through the interfacial insulator layer between the metal and the semiconductor can be described by traditional thermionic emission (TE) theory [1, 2]. Thermionic emission over the potential barrier is one of the carrier transport mechanisms. That is, this theory assumes that the current flow depends on the barrier height. TE method is one of the most common approaches used to determine diode electronic parameters such as saturation current, ideality factor, and barrier height. For this, the forward bias current–voltage (I–V) characteristics are used.

Silicon nitride (Si3N4), which is an excellent ion diffusion barrier, is one of the most promising insulators. The low leakage current, high dielectric constant, and larger energy gap are some of the properties of silicon nitride. However, silicon nitride is used in electronic and industrial applications due to the excellent electrical and thermomechanical properties. The silicon nitride film as an insulator or dielectric can be prepared by different techniques to illustrate atomic layer deposition (ALD), magnetron sputtering, and chemical vapor deposition (CVD) [8,9,10].

In this paper, we fabricated the Au/Si3N4/p-GaAs (MIS) diode. The electronic parameters of the MIS diode. The forward bias I–V characteristics were used to obtain electrical parameters such as ideality factor, and barrier height, interface state density, and series resistance of the MIS diode. At the same time, the barrier height was compared by using TE and Norde methods. The forward and reverse bias I–V characteristics were also used to determine the current conduction mechanisms of the diode.

2 Experimental details

To fabricate the MIS diode, zinc (Zn)-doped p-type gallium arsenide (GaAs) single crystal wafer with (100) surface orientation, having carrier concentration of 1017–18 cm−3 and thickness of 500 μm was used. Before coating, the p-GaAs wafer were subjected to a chemical cleaning procedure in organic solvents. To remove the undesirable surface impurities, the wafer was washed in 5H2SO4:H2O2:H2O acidic solution for 1 min followed by etching in H2O:HCl solution. The wafer was then rinsed with deionized water having 18 MΩ cm. Finally, to avoid surface oxidation, the wafer was dried with pure nitrogen. After the cleaning and etching process, high purity gold (Au) metal and metal evaporation system were used for ohmic contact. The 2000 Å contact at the back of p-GaAs wafer was prepared by thermal evaporation of Au at 375 °C with 3 × 10–6 Torr vacuum. Then, the wafer was annealed at 475 °C for 7 min in nitrogen. After preparing the ohmic contact, the wafer was loaded into a radio frequency (RF) reactive magnetron sputtering system and heated up to 400 °C. Afterwards, the wafer was transferred into the deposition chamber to deposit silicon nitride (Si3N4) film from Si3N4 target, under specific Ar/O2 reactive gas mixture (Ar/O2 = 90/10 sccm) controlled by mass flow controllers. During the Si3N4 thin film deposition, the wafer temperature and the pressure were set to 200 °C and 3 × 10–6 mbar, respectively. After coating of the Si3N4 film, the 2000 Å rectifier contact was prepared by thermal evaporating of Au on the Si3N4/p-GaAs as dots with the contact area of 7.85 × 10–3 cm2 at 30 °C. Thus, the Au/Si3N4/p-GaAs (MIS) diode was fabricated. The surface morphology of Si3N4 film was characterized by a NanoMagnetics Instruments atomic force microscopy (AFM) system. The I–V measurements of the fabricated diode were performed at room temperature by the use of a Keithley 2400 sourcemeter.

3 Results and discussions

3.1 AFM analysis

The surface morphology of Si3N4 film grown on GaAs substrate was analyzed by atomic force microscopy (AFM). The 2D and 3D AFM images of scan area of 2 μm × 2 μm are given in Fig. 1a and b, respectively. The route mean squared (RMS) value is a measure of surface roughness. From the AFM analysis, the RMS value is found to be 0.24 nm. This value is less than one nanometer. As a result, the AFM image confirms that the film is quite smooth.

Fig. 1
figure 1

The surface morphology of Si3N4 film deposited on GaAs substrate a 2D and b 3D AFM images with 2 μm × 2 μm scan area

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3.2 Electrical analysis

Thermionic emission (TE) is one of the current conduction mechanisms occurred in Schottky barriers. The current is transported via thermionic emission over the potential barrier. In the TE theory, I–V characteristics for forward bias voltages larger than 3kT/q may be analysed as follows [1, 2]

$$I={I}_{o}\mathrm{e}\mathrm{x}\mathrm{p}\left(\frac{q\left(V-I{R}_{\text{s}}\right)}{nkT}\right)$$
(1)

where Io is the saturation current, V − IRs is the voltage drop across Rs, and n is the ideality factor. The n and I0 values can be derived from slope and intercept of the linear region of the forward bias ln(I) − V curve, respectively. Thus, I0 and n are given as follows:

$${I}_{\text{o}}=A{A}^{*}{T}^{2}\mathrm{e}\mathrm{x}\mathrm{p}\left(-\frac{q{\Phi }_{\text{bo}}}{kT}\right)$$
(2)

and

$$n=\frac{q}{kT}\left(\frac{{\text{d}}V}{{\text{d}}\left(\mathrm{I}\mathrm{n} I\right)}\right)$$
(3)

where Φbo is the zero-bias barrier height calculated from Eq. 2, A is the area of the MIS diode and A* is the Richardson constant (= 74.4 A/cm2 K2 for p-GaAs).

Figure 2 demonstrates forward and reverse bias I−V plot of the Au/Si3N4/p-GaAs (MIS) diode at room temperature. It is clear that the MIS diode exhibits a good rectifying behavior. The rectification ratio (RR = IF/IR) value is found to be 2.45 × 104 at ± 4 V. As seen in Fig. 2, this plot deviates from the straight line due to the series resistance (Rs) at high forward bias. The I0, n and Φb0 value are found to be 3.57 × 10–9 A, 2.41, and 0.79 eV, respectively. The ideality factor must be equal to 1 for an ideal Schottky barrier diode or homogeneous interface. The barrier inhomogeneous, recombination-generation, tunneling, interface impurities, series resistance, and interface states may cause to have ideality factor larger than unity [11,12,13,14,15,16,17].

Fig. 2
figure 2

The I−V plot of the MIS diode

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To obtain shunt (Rsh) and series (Rs) resistance of the MIS diode, Ohm’s law (Rj = dV/dI) was used [18]. The Rsh was obtained at very high reverse bias where the junction resistance (Rj) value stays almost constant. On the other hand, the Rs resistance was obtained at very high reverse bias in which the Rj has a constant value. Figure 3 demonstrates the Rj–V plot of the diode. The Rsh and Rs value at − 4 V and + 4 V are found to be 9.96 MΩ and 0.42 kΩ, respectively.

Fig. 3
figure 3

Rj−V plot of the MIS diode

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To derive the Φb and Rs value of the diode, another method proposed by Norde was used [19]. F(V) identified as Norde function is given as follows:

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

where γ (4 > n) is an integer greater than the obtained n value (= 2.41). According to this method, firstly F(V)–V curve is plotted, and then the Φb and Rs value are calculated using the following equations,

$${\Phi }_{\text{b}}=F\left({V}_{\min}\right)+\frac{{V}_{\min}}{\gamma }-\frac{kT}{q}$$
(5)
$${R}_{\text{s}}=\frac{kT(\gamma -n)}{q{I}_{\min}}$$
(6)

where F(Vmin) is the minimum point of the F(V)−V plot and Imin is the current corresponding to Vmin value. Figure 4 shows the F(V)−V plot of the diode. The F(V)−V plot gives a minimum value. The Φb and Rs values are found to be 0.81 eV and 5.11 kΩ, respectively. It is found that the Φb value obtained by the Norde method is harmonious with the one obtained by the TE method.

Fig. 4
figure 4

F(V)−V plot of the MIS diode

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The interface states are another parameter that is significantly effective on the I−V characteristics. The interface state density (Nss) of the MIS diode was calculated using method proposed by Card and Rhoderick [20]. According to this method, NSS is expressed as follows:

$${N}_{\text{ss}}\left(V\right)=\frac{1}{q}\left[\frac{{\varepsilon }_{\text{i}}}{\delta }\left(n\left(V\right)-1\right)-\frac{{\varepsilon }_{\text{s}}}{{W}_{\text{D}}}\right]$$
(7)

where εi (= 7.8) and εs (= 12.9) are permittivity of Si3N4 and GaAs substrate, respectively. In addition, δ (= 65 Å) is the thickness of Si3N4 layer and WD (= 4.09 × 10–5 cm) is the depletion layer width obtained from C−2−V plot (not given here) at 1 MHz. For p-type semiconductor, the relation between the energy of interface states (ESS) and the top of the valence band energy (EV) is given by,

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

Φe, which is the effective barrier height, and n(V) are given as follows, respectively, [20,21,22,23,24,25,26]

$${\Phi}_{\text{e}}={\Phi}_{\text{bo}}+\left(1-\frac{1}{n\left(V\right)}\right)V$$
(9)
$$n\left(V\right)=\frac{qV}{kT\ln\left(I/{I}_{\text{o}}\right)}$$
(10)

The NSS vs. ESS − Ev plot of the MIS diode is given in Fig. 5. It has been seen that the NSS value is decreased with increase in ESS − Ev. However, the NSS value rises with bias from the mid gap towards the top of the valence band.

Fig. 5
figure 5

NSS versus ESS−Ev plot

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To determine the dominant current conduction mechanisms such as ohmic behavior, space charge limited current (SCLC) and trap charge limited current (TCLC) of the MIS diode, the In(IF) versus In(VF) curve was drawn under forward bias and given in Fig. 6. It is clear that the curve indicates three linear regions called as the Region 1 (− 3.00 ln V   ≤ − 1.61), Region 2 (− 1.39 ln V ≤ − 0.29) and Region 3 (− 0.22 ln V ≤ 1.39). I − V characteristics of a diode obey to a power law given by I ∼ Vm [25,26,27,28,29,30,31]. The magnitude of m indicates the dominant current transport mechanism and is calculated from the slope of In(IF) vs. In(VF) curve. For Region 1, Region 2, and Region 3, the m values are found to be 1.12, 6.26, and 2.39, respectively. At the Region 1 or the low voltage range, the value of m is close to one. This result shows that the dominant transport mechanism is the ohmic-like behavior or conduction. This case is related to the injected of charge carriers from the electrode into semiconductor material. At the Region 2 or the intermediate voltage range, the m value is higher than two. In this case, the dominant mechanism is the trap charge limited current (TCLC) mechanism. This result indicates the existence of an exponent trap distribution. At the Region 3 or the high voltage range, the dominant mechanism is the space charge limited current (SCLC) mechanism. Such behavior is due to the increasing number of injected electrons from the electrode causing filled trap states in the space charge region.

Fig. 6
figure 6

In(IF) versus In(VF) curve

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In addition, to analyze mechanisms dominating the current conduction in the MIS diode, the In(IR) versus VR0.5 curve was drawn under reverse bias and given in Fig. 7. The Poole–Frenkel emission (PFE) and Schottky emission (SE) mechanisms were considered to determine the reverse current mechanism. The reverse current due to the PFE is described as follows [31,32,33,34,35,36]:

Fig. 7
figure 7

In (IR) versus VR0.5 curve

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$${I}_{\text{R}}={I}_{o}\mathrm{e}\mathrm{x}\mathrm{p}\left(\frac{{{\beta }_{\text{PF}}V}^{1/2}}{kT{d}^{1/2}}\right)$$
(11)

However, the reverse current due to the SE is described as follows:

$${I}_{\text{R}}=A{A}^{*}{T}^{2}\mathrm{exp}\left(\frac{-{\Phi }_{\text{b}}}{kT}\right)\mathrm{e}\mathrm{x}\mathrm{p}\left(\frac{{\beta }_{\text{SC}}{V}^{1/2}}{kT{d}^{1/2}}\right)$$
(12)

where βPF and βSC are field-lowering coefficients of the PFE and SE, respectively. The relation between the two coefficients is given as follows:

$$2{\beta }_{\text{SC}}={\beta }_{\text{PF}}={\left(\frac{{q}^{3}}{{\pi \varepsilon }_{\text{o}}{\varepsilon }_{\text{i}}}\right)}^{1/2}$$
(13)

where εi (= 7.8) and εo (= 8.85 × 10–14 F/cm) are the dielectric constant of Si3N4 and vacuum, respectively. Using the εi and ε0 values, the theoretical values of βPF and βSC were obtained as 5.43 × 10–4 eVm1/2 V−1/2 and 2.72 × 10–4 eVm1/2 V−1/2, respectively. It is clear that the curve indicates two linear regions called as the Region 1 (2.00 ≤ V0.5 ≤ 1.52) and Region 2 (1.50 ≤ V0.5 ≤ 0.22). At the Region 1, the experimental value of field-lowering coefficient, β, is found to be 1.17 × 10–5 eVm1/2 V−1/2. At the Region 2, the experimental value of β is found to be 3.66 × 10–5 eVm1/2 V−1/2. The obtained experimental values are close to the theoretical value of Schottky emission, βSC. This result confirms that the reverse current conduction in the MIS diode is Schottky emission.

4 Conclusion

The electrical characteristics and current conduction mechanisms of the Au/Si3N4/p-GaAs (MIS) diode have been studied at room temperature. Based on the thermionic emission (TE) theory, the I–V characteristics of the MIS diode have been explained. Basic diode parameters such as Φbo, n and Rs of the MIS diode were obtained from TE method. The Φb value was also determined from Norde method to compare with the value obtained from TE method. The barrier height values were found to be in harmony with each other. Besides, the value of Nss was calculated from the forward bias I–V measurement. In addition, the current conduction mechanisms of the MIS diode have been analyzed by using both forward and reverse bias I–V measurements. Under forward bias, the current conduction is associated with ohmic, TCLC, and SCLC mechanisms. Under reverse bias, the current conduction is associated with the SE mechanism. The obtained results suggest that the fabricated MIS diode will also be suitable for capacitor applications.