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Dielectric properties and capacitance –voltage of GO/TiO2/Si junction were investigated in frequency range (10-2x107Hz) and temperature (-40- 90°C). Dependence of έ, ε՜՜ , tan δ, real and imaginary parts of electric modulus (M՜ & M՜՜), impedance and ac conductivity on frequency and temperature were studied. From results it is found that έ increases with increasing frequency at low frequency region while that it decreases at high frequencies. ε՜՜ decreases with frequency (ν) increment in the range (10- 56Hz) & (1619-12195Hz). It is observed that decrement of 𝑡𝑎𝑛𝛿 with increasing frequency in higher range (1355210 -2x107 Hz).

Real part of electric modulus (M՜) decrease with increasing frequency. AC conductivity increases with increasing temperature.

Moreover, activation energy (Ea) values decrease with increasing ν then increase at higher ν.

Different parameters, like as, built-in potential, carrier density, image force lowering and barrier height were derived from the reverse bias C-2 –V curves. It is found that, built–in–voltage (Vbi) , barrier height (φb) and Fermi energy (EF) increase with increasing temperature. Moreover, donor concentration (ND) and image force barrier lowering (∆φb) decrease with temperature increment. In addition, series resistance (Rs) decreases with temperature and frequency increment.

Investigation of dielectric and electrical materials are still attractive topic among the scientists because of their important roles in electronic devices [1] like as diode [2, 3], transistor [4], light emitting diode [5] and energy storage/convergence, sensor, membrane, catalysis. MOS structures are considered a type of capacitor, which stores the electric charge by virtue of dielectric property of insulator or oxide layers. The frequency and temperature are more eﬀective on electrical and dielectric properties of electronic devices.

At low temperatures, these devices aren’t enough free charges and many of them may be frozen. When the temperature becomes increases, more and more carriers electron or holes can be passed on the top of barrier height and so yield an excess capacitance and conductance to measure of them [6–9]. Similarly, at low frequencies surface states can easy follow the alternating signal and yield an excess capacitance and conductance to measure of them. Titanium dioxide (TiO2) is important in industry because of its wide applications in microelectronics, solar cells, memory devices and photonic crystals [10, 11].

TiO2 has dielectric constant ranging from 16 to 100, n-type semiconductor with a wide band gap 3.5 eV and refractive index ≈ 2.6 and has stability with Si [12]. In this work, the target is studying applied voltage, frequency and temperature effects on both real and imaginary parts of dielectric constants (έ & ε′′), loss tangent (𝑡𝑎𝑛𝛿), ac electrical conductivity (𝜎𝑎𝑐), impedance and electric modulus (𝑀′ and 𝑀′′). Also, investigating the influence of temperature and frequency on capacitance- voltage and calculating some parameters like barrier height, built- in–voltage, Fermi energy, carrier density, and image force lowering of GO/TiO2/Si junction.

Real part of dielectric constant (έ) represents a capacitive behavior or polarizability of the material, and an imaginary part (ε′′) shows energy losses attributed to polarization and conduction. Fig.2a clarifies variation of έ with applied voltage from -2V to +2V at different low frequency (ν = 10 -78.4 Hz) and at temperature 273K for GO/TiO2/Si MOS junction. It is noticed that έ increases with increasing ν and all values of έ are negative. This is attributed to the capacitance and dielectric constant values are directly proportional to each other according to this relation:

έ = (1)

Where Cº is capacitance of an empty capacitor, Cº = εº(B/d) where B is a rectifier contact area in cm-2, d is interfacial insulator layer thickness and εº is permittivity of free space charge and Cm is measured capacitance. In the work we have done before, capacitance values are found to be negative in low frequency region. At high frequency region (968005- 2x107 Hz), it is obvious that έ decreases with frequency increment as seen in Fig.2b. It is known that έ may be affected by four types of polarization processes (electronic, ionic, dipolar, and interfacial) at low frequencies but at high frequencies (f ≥1010 Hz) the supporting of electronic and ionic parts becomes dominant only.

Moreover έ values depend on several factors such as substrate temperature, annealing, frequency, the growth or preparation methods, thickness and homogeneities, applied voltage or electric field [13-17]. Relation between ε′′ and voltage at different low and high frequencies (10- 56Hz) & (1619-12195Hz) at T = 273K is illustrated in figure 2(c &d). It is obvious that a decrement of ε′′ with increasing ν. This may be due to when the frequency increased; interfacial dipoles have less time to orient themselves in direction of the alternating field [18-23]. Moreover, ε′′ values are greater at low frequencies may be attributed to the presence of a possible interface polarization mechanism since interface states cannot follow the ac signal at high frequencies and do not contribute to the capacitance, ε′′ values due to the lack of any interface polarization mechanism[24].

In addition, loss tangent, related to (ε′′& έ) by the relation: 𝑡𝑎𝑛𝛿 = ε′′/ έ = Gm/ωCm. Where Cm is measured capacitance and conductance (Gm/ω), ω= is angular frequency, έ is denoted by equation 1 and ε′′ is defined by ε′′= Gm/ωCº. 𝑡𝑎𝑛𝛿 points out to the amount of energy that is wasted in dielectric when an electric field is applied across it [25, 26]. Fig.2e represents the characteristics of 𝑡𝑎𝑛𝛿 with voltage at low frequency range (10- 78Hz) and at T = 273K. We see that negative values of 𝑡𝑎𝑛𝛿 and this interpreted on frequency dependence of έ where it has negative values at low ν. At high frequency range (1355210 -2x107 Hz), variation of 𝑡𝑎𝑛𝛿 with applied voltage is shown in Fig.2f. It is noticeable that a decrement in 𝑡𝑎𝑛𝛿 with increasing ν. Electric modulus formalisms (M*) explained by Macedo et al. [27], both real and imaginary electric modulus (M՜& M՜՜՜) calculated from έ & ε′′:

M*= =, i = (-1)1/2 (2)

Fig.3a shows dependence of M ՜on voltage at different low frequencies (10- 56Hz) at T = 273Kfor GO/TiO2/Si MOS junction. We see that a decrease of M՜ with increasing ν, also decreases with negative dc bias voltage and then increases at positive voltage bias. According to equation 1, M՜ is in inverse relation with έ. At high frequency range (968005 – 2x107 Hz) at T = 273K, M՜ decreases with increasing ν as shown in figure 3b. Fig.3(c &d) represent the relation between M՜՜՜ and different frequencies at T =273K. We noticed that a decrement in M՜՜՜ with increasing ν and symmetric change in M՜՜՜ due to the effect of polarization.

Moreover, the change in electric modulus is a result of restructuring and reordering of charges at the interface under external electric field or voltage and interface polarization [28]. Also, at lower frequencies the real and imaginary part of electric modulus exhibit low value which may be attributed to the large value of capacitance associated with the electrode polarization and at high frequency it shows high values as a consequence of low value of capacitance [29]. Series resistance (Rs) is one of significant sources of small energy loss in devices such as metal semiconductor (MS), metal-insulator-semiconductor (MIS), photodetectors and solar cells. Graph 4a shows a relation between series resistance (Rs) and applied voltage at different low frequencies (10- 590Hz). It is observed that increment till 0.0 volt and then decreases with increasing voltage and Rs decreases with increasing frequency. Also at high frequency (65592-493880Hz), Rs decreases with frequency increment as shown in Fig.4b. Real part of ac conductivity (σac) is calculated by using the expression:

Where 𝜔 is the angular frequency, εₒ is free space permittivity (8.85×10−12 Fm−1), is dielectric constant and is dielectric loss tangent. Frequency dependence of Rs is attributed to the particular distribution of interface state density (Nss), interfacial layer, and restructuring and the reordering of dipoles under an applied voltage. Variation of (σac) with applied voltage at frequency range (10.4- 826 Hz), at room temperature shows a decrease with increasing ν and decreases with increasing the voltage from -2 to 0.0 Volt and then increases with the increase of voltage from 0.0 to +2 volt as seen in Fig. 4c. Figure 4d represents a dependence of σac on applied voltage at different ν (968005 – 2x107 Hz) at T=273K. It is noticed that a slight decrease in σac with increasing ν, it is clear that is in close relation with conductivity. As seen in equation 3, σac depends upon. In addition, it is observed in Fig.2b, decreases with increasing ν and accordingly, σac decreases where it is suggested that the decrease in ac conductivity with increasing frequency is attributed to the series resistance effect [30].

Impedance is an important to understand of the conducting mechanism and electrical properties of materials. Impedance of junction can be estimated by using the equations [31]

Z(Jω) = Z՜ - JZ̎ =

= (4)

Z՜=, (5)

Where ω = 2πf is angular frequency, R, C and Cₒ are resistance, capacitance and capacitance of vacuum respectively [32]. The variation of real part impedance with frequency gives the information about the frequency dependence of ac conductivity of the material. According to Fig. 4(e,f) real impedance (Z ́) values are high in low frequencies (10-109.7Hz) and these values decrease as the frequency increase (65592 – 691432Hz). Moreover, it is observed that Z ́ increases with increasing ν then reaches a maximum at 0.0 volt and then decreases with increasing ν at low frequency region. At high ν, Z ́ decreases with the increase of ν in applied voltage range (-2- 2V) at room temperature.

Decrement in Z′ with increasing ν may be attributed to space charge polarization effect in the material. Generally, space charges are created in the material due to the disparity in concentration and inhomogeneity of the applied field, which hinders the fast recombination of the charge carriers [30]. Therefore, the space charges present in samples might be trapped well in grain boundary and grain–electrode interfaces. Variation of imaginary part of impedance (Z̎) with applied voltages at low frequency (10.4- 154 Hz) and T = 273K is shown in Fig.5a.

We noticed that Z̎ decreases with increasing frequency, increases with voltage increment at inversion region (-2 - 0V) till reaches maximum at depletion region (0V) and then decreases at accumulation region (0- 2V). It may be due to a slow relaxation process in the material, there has been decrease in value of Z′′ with increasing frequency and that may be attributed to space charges polarization. Also, the electrical conduction in the low frequency region is attributed to short range translational hopping and thus the contact resistance may induce significant current variation. At high frequency range (986005 – 2x107 Hz), T= 273K and voltage (-2- +2V), it is noticed that a negative Z′′ values as shown in Fig. 5b. The changing in the impedance value is related to the presence of the movement paths of the mobility charge carriers [33, 34].

At depletion region (0V), T (-40 – 90C°) and low frequency range (10-153.6Hz), dielectric constant (ε՜) decreases with increasing frequency and temperature, ε՜՜ values decrease with increasing ν whereas increase with temperature increment and tanδ increases with temperature and decrease with increasing frequency as observed in table 1. It is noticeable that tan δ increment with rising temperature indicating semiconductor behavior. The negative dielectric constant has been calculated from the negative capacitance.

This negative ε՜ obtained from negative capacitance (NC) may be also due to the space charges located at grain boundaries in the materials also to the contribution of dipolar polarization effects at low frequency. Dielectric loss factor (tanδ) of junction can be interpreted as the ratio of the energy dissipated in the material to the energy stored and it determines the mechanism of ac conduction and dielectric relaxation. Variation of tanδ with temperature may be attributed to space polarization caused by impurities or interstitials in semiconductor and metal.

At high frequency (8.711x103- 2x107), T (-40- 90°C) and (0V), έ increases with T and ν increment as seen in Table . The application of electric ﬁeld creates static dipoles in the material. Since the electric ﬁeld changes its polarity with time. As the frequency increases, dielectric permittivity slightly decreases because lateness dipoles behind the ﬁeld. Moreover, at high temperature, polarization occurs due to free movement of charge carriers through the crystal. The higher values of έ at low frequencies are due to the accumulation of free charges at the grain boundary, whereas, the low έ values at high frequency is attributed to the lower dielectric constant of the grains [35-37].

The value of M' is very small in low frequency region, but increases with increasing frequency at all temperatures as illustrated in table . As the temperature rises, imperfections/disorders are created in the lattice and the mobility of the majority charge carriers increases [38-41]. So, this eﬀect causes increasing in values of ε՜՜ with increasing temperature. From table 1 at temperature and frequency range (-40-90°C), (10-2x107Hz) in the depletion region (0V), it can be seen that the values of Z' has higher values at low temperatures and low frequency regions while its value decreases with frequency (ν) increment. Moreover, there is inverse relation between Z' and temperature. When the temperature increases the real part of impedance (Z') decreases, which shows the fact that the ac conductivity increases due to the increasing charge mobility. In addition, such a behavior is very common in dielectric materials [34- 41]. Also, at the same range of ν and temperature it is observed that the magnitude of Z'' decreases as both temperature and frequency increase, which indicates the fact that the ac conductivity increases as frequency increases.

The complex conductivity (σ*) can be given by:

σ*= J εº ωε* =J εº ω(έ-Jε՜՜) = εº ω ε՜՜+ J εº ω έ (6)

From table , it is clear that both real and imaginary parts of ac conductivity increase with temperature increment. Similar results have been reported in the literature [42-45], it is suggested that the process of dielectric polarization in MOS junction takes place through a mechanism similar to the conduction process. Also, the increase in electrical conductivity at low temperature is attributed to the impurities, which reside at the grain bound aries [46-49].

These impurities lie below the bottom of the conduction band and thus it has small activation energy. This means that the contribution to the conduction mechanism comes from the grain boundaries while it mainly results from the grains for higher temperatures. At higher frequencies, the conductivity indicates strong frequency dependence. This can be attributed to the result of a decreasing series resistance with increasing frequency. Fig.5c represents the relation between lin σAC and 1000/T at depletion region (0V) and different frequencies (968005- 5x107Hz). We noticed that a linear relation decreases with increasing ν and increases with increasing temperature. By using the following Arrhenius equation, the activation energy can be estimated [48, 38, 50]:

σ (T) = σº exp (7)

Where σº, q, k and Ea are pre-factor, electronic charge, Boltzmann constant and activation energy respectively. The relation between Ea and frequency is clarified by figure 5d. It is obvious that Ea values decrease with increasing ν then increase at higher ν and tabulated at table .

Capacitance–voltage (C–V) temperature–dependent measurement is important method that can give information about the built–in–voltage, Fermi energy, carrier density, and image force lowering and barrier height. Fig. 6 shows the relation between (1/C2) and applied voltage (-1.5- 0.0V) at ν =12195 Hz and T (233- 363K). It is observed that 1/C2 increase linearly with increasing temperature and with increasing voltage. Capacitance of GO/TiO2/Si MOS junction can be given by [51]:

C = (8)

Where ND, Vbi,V, εs and ε0 is donor concentration, built–in–voltage at zero bias, reveres bias voltage, dielectric constant and vacuum permittivity (ε0 =8.85×10–12 F/m) respectively [52]. Firstly, we can calculate Vbi and ND, the barrier height (φb), Fermi energy (EF), image force barrier lowering (∆φb) and effective carrier density (NC) can be calculated from the following relations [53,54]:

Φ(C-V) = (9)

Φ(C-V) = Vbi + (10)

Where V0 is the intercept of C–2 with voltage axis and is related to Vbi. EF is the Fermi energy is given by:

ln( (11)

All the calculated values are listed in Table . From this table, it is observed that Vbi , EF and φb values increase with increasing temperature but ND and ∆φb decrease with temperature increment. It is also observed that the barrier height increases due to image force barrier decreases at higher temperature. The series resistance (Rs) is estimated by using the following equation [55, 56]:

Where Cma and Gma are measured capacitance and conductance. As seen in table , at frequency (10 – 2x107), T ( -40- 90ºC) and (0V) , Rs decreases with increasing temperature and frequency. This may be due to restructuring and reordering of interface due to the temperature effect [44].

In summary, dielectric properties and Capacitance- voltage of GO/TiO2/Si MOS junction is investigated as a function of frequency and temperature. It is found that lowering ε՜ with increasing frequency and temperature, ε՜՜ values decrease with ν increment whereas increased with temperature increment and tanδ increases with temperature and decreased with increasing frequency. At high ν, Z ́ decreased with the increase of ν in applied voltage range (-2- 2V) at room temperature.

Moreover, it is obvious a linear relation between lin σAC and 1000/T decreased with ν increment and risen with rising temperature. Activation energy (Ea) decreased with increasing ν then increase at higher ν. From C–2-voltage relation, it is observed that Vbi , EF and φb values increased with increasing temperature. ND and ∆φb reduced with temperature increment. Lower Rs with temperature increment may be attributed to restructuring and reordering of interface.

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