## Abstract

RF magnetron sputtering was used to grow silicon nitride (Si_{3}N_{4}) thin film on GaAs substrate to form metal–oxide–semiconductor (MOS) capacitor. Complex dielectric permittivity (ε*), complex electric modulus (M*) and complex electrical conductivity (σ*) of the prepared Au/Si_{3}N_{4}/p-GaAs (MOS) capacitor were studied in detail. These parameters were calculated using admittance measurements performed in the range of 150 K-350 K and 50 kHz-1 MHz. It is found that the dielectric constant (ε′) and dielectric loss (ε″) value decrease with increasing frequency. However, as the temperature increases, the ε′ and ε″ increased. Ac conductivity (σ_{ac}) was increased with increasing both temperature and frequency. The activation energy (E_{a}) was determined by Arrhenius equation. Besides, the frequency dependence of σ_{ac} was analyzed by Jonscher’s universal power law (σ_{ac} = Aω^{s}). Thus, the value of the frequency exponent (s) were determined.

## Introduction

Metal-oxide-semiconductor (MOS) structure consisting of an oxide layer between the metal contact and semiconductor substrate is used in various semiconductor device applications such as MOS capacitor (MOSCAP), MOS field effect transistor (MOSFET), MOS sensors, MOS integrated circuit (MOS IC) and MOS memory [1,2,3,4]. Especially, MOS capacitor forms the basic building block of the MOSFET. Also, in the MOS capacitor fabrication, an ohmic contact to the back of the semiconductor forms with a second metal layer. Several regimes such as accumulation, depletion and inversion of the MOS capacitor can be obtained by varying the applied bias voltage. The MOS capacitor is composed of a series connection of two capacitors such as the oxide layer capacitor and the depletion layer capacitor. The MOS capacitors have been characterized using capacitance-voltage (C-V) and conductance-voltage (G-V) measurements. Electrical parameters such as oxide (dielectric) thickness, interface trap densities, series resistance, barrier height, charges in the oxide, and doping concentration of MOS structure can be extracted from the admittance (Y = G + iωC) measurements. Among them, the interface states (N_{ss}), and series resistance (R_{s}) are important parameters affecting performance and electrical characteristics of the MOS device.

The oxide in MOS structure is used as the dielectric. Due to the dielectric property of the oxide, MOS structure is equivalent to a parallel plate capacitor. A dielectric material is polarized under the influence of an external electric field. In this way, a dipole moment occurs. The polarization mechanisms such as electronic, ionic, orientational and interfacial observed in dielectric materials depend on both material structures and frequency and temperature conditions. Therefore, the major factors such as oxide layer thickness, the homogeneity of the oxide, frequency of applied alternating electric field, and temperature lead to a change in dielectric properties of MOS capacitor. Dielectric parameters such as dielectric constant (ε′), dielectric loss (ε″), dielectric loss tangent (tanδ), electrical conductivity, and electric modulus can be determined from the admittance measurements [5,6,7,8].

Silicon nitride (Si_{3}N_{4}) is one of the most promising insulating layers. Si_{3}N_{4} possess excellent properties such as high wear resistance, high flexural strength, high creep resistance, high fracture resistance, high temperature stability, low thermal expansion coefficient, low leakage current, high dielectric constant and larger energy gap. Especially, Si_{3}N_{4} is used as ceramic material in the engineering field due to its important mechanical, thermal and electrical properties. Si_{3}N_{4} is also used as thin film material in the role of insulator/dielectric layer, optical coating, diffusion barrier. Besides, Si_{3}N_{4} thin film can be formed on semiconductors (Si, Ge, and GaAs) using various techniques including atomic layer deposition (ALD), physical vapor deposition (PVD), magnetron sputtering, and chemical vapor deposition (CVD) [9,10,11,12].

In this study, silicon nitride (Si_{3}N_{4}) as interfacial oxide/dielectric layer between Au and GaAs was used. Thus, Au/Si_{3}N_{4}/p-GaAs (MOS) capacitor was fabricated. Firstly, the admittance measurements of the prepared MOS capacitor were carried out in a wide frequency and temperature range. Then, dielectric parameters of the MOS capacitor were determined using the measured capacitance and conductance data. The obtained experimental results were analyzed in detail.

## Experimental details

Silicon nitride (Si_{3}N_{4}) thin film has been prepared on Zn-doped p-type GaAs single crystal wafer to fabricate an Au/Si_{3}N_{4}/p-GaAs (MOS) capacitor by RF magnetron sputtering system. In our previous article [13], more information on fabrication processes was given. The interfacial Si_{3}N_{4} layer thickness was estimated to be about 175 Å from the oxide capacitance (C_{ox}) in the strong accumulation. Besides, the surface area of capacitor or contact was determined to be 7.85 × 10^{–2} cm^{2}.

Admittance measurements (capacitance and conductance) of the prepared MOS capacitor were taken using a HP 4192A LF impedance analyzer. The reverse and forward bias C-V and G-V measurements were carried out in the wide range of dc voltage (± 8 V) by 100 mV steps. At the same time, these measurements were performed in the frequency range of 50 kHz–1 MHz and in a wide temperature range from 150 to 350 K. The capacitor temperature was controlled by Janes vpf-475 cryostat. Moreover, the temperature was monitored by measuring with a dmm/scanner Keithley model 199 and Lake Shore model 321 auto-tuning temperature controller.

## Results and discussion

### Admittance measurements

Admittance (Y = G + iωC) measurements are obtained from a capacitance (C) in parallel with a conductance (G). The admittance measurements were carried out separately at four frequencies (50, 100, 500 and 1000 kHz/1 MHz) and six temperatures (150, 200, 250, 300, 325 and 350 K). The variations of C and G with frequency at various temperatures are presented in Fig. 1a and 1b, respectively. As seen in Fig. 1a, c value decreases with increasing frequency. This is due to the existence of the interface states and leakage current [1, 2]. At high frequencies, the interface states cannot follow ac signal and do not contribute to the capacitance. Also, for each frequency, the C value increases with increasing temperature.

As seen in Fig. 1b, *G* value increases with an increase in frequency. Besides, at each frequency, the *G* value was increased with an increase in temperature. As the temperature increases, the additional thermal energy increases the number of thermally generated carriers. Thus, minority carrier concentration increases with temperature. Moreover, the temperature increase causes in an increased electrical conductivity. As a result, temperature changes have significant effects on the capacitance and conductance [14,15,16].

### Complex dielectric permittivity

The complex dielectric permittivity (ε* = ε′−iε″) of a dielectric material is composed of two parts, where ε′ and ε″ are the real part (or dielectric constant) and imaginary part (or dielectric loss), respectively [5,6,7, 17, 18]. The ε′ and ε″ represent the stored energy within the dielectric and the dissipated or loss energy resulting from the rotation of the dielectric atoms or molecules in an ac electric field, respectively. The dielectric permittivity depends on various factors such as frequency, temperature, and structure of dielectric material. In the case of admittance (Y) measurements, the ε* formula is given as,

where C_{m} and G_{m} are the measured capacitance and conductance, respectively. ω(= 2πf) is the angular frequency and C_{0} (= ε_{0}A/d) is the capacitance of an empty capacitor. ε_{0} (= 8.85 × 10^{–14} F/cm) is the dielectric permittivity of free space. The ε′ and ε″ were extracted from Eq. 1. Their values can be calculated from the following relations [6, 7],

and

The ratio of the ε″ to the ε′ is called dielectric loss tangent represented by tan. Here, δ is called the loss angle and is the phase difference between the current in the dielectric material and the applied ac field. The tan is given by,

The variation of ε′, ε″ and tanδ with temperature as a function of frequency is plotted in Fig. 2a–c, respectively. As seen in Fig. 2a, b, the ε′ and ε″ with frequency exhibit a similar behavior with the capacitance and conductance. The value of ε′ and ε″ decreases with an increase in the frequency in the entire temperature range. As the frequency increases, the interfacial dipoles have less time to orient themselves in the direction of the alternating electric field. This case can contribute in increasing net dipoles on interface. Besides, the high value of ε′ at low frequencies is due to the accumulation of free charges at the interface. It is clear that the interfacial and orientation polarization dominate at low frequencies [19,20,21,22,23]. In addition, it is seen that both ε′ and ε″ increase with increasing temperature. As the temperature increases, the orientation of dipoles become more facilitated. Hence the orientation polarization increases. This may cause an increase in the ε′ value. On the other hand, the number of charge carriers increases exponentially with increasing temperature and thus leading to an increase in the ε′ and ε″ [19,20,21,22,23,24,25,26]. The obtained results for the Au/Si_{3}N_{4}/p-GaAs (MOS) capacitor were found to be consistent with those reported in the literature [19,20,21]. As seen in Fig. 2c, the tanδ is dependent on both temperature and frequency. As the frequency increases, dipoles cannot follow the alternating field. Therefore, the tanδ decreases with increasing frequency.

### Complex electric modulus

The electric modulus corresponds to the relaxation of the electric field in the dielectric material. Complex electric modulus (M*) consists of two parts and is defined as follows:

Here, the first term represents the real (M′) part and the second term represents the imaginary (M″) part. The M′ and M″ values were calculated from the obtained ε′ and ε″ data. Figure 3a, b show the variation of M′ and M″ at various temperatures as a function of frequency, respectively. As seen in Fig. 3b, the M″ value increases with increasing frequency. However, at higher frequencies, its value increases with increasing temperature. This is due to the short range mobility of charge carriers. The increase of M′ and M″ with frequency is attributed to the mobility of charge carriers under the action of an induced electric field [25,26,27,28,29,30,31].

### Complex electrical conductivity

Complex electrical conductivity (σ*) is given by the following relation,

The real part of the σ* is defined as ac electrical conductivity (σ_{ac}). The σ_{ac} value can be calculated from the complex dielectric permittivity values and is given as follows,

Figure 4 shows the variation of ac conductivity(σ_{ac}) with frequency at various temperatures. As shown in Fig. 4, the value of σ_{ac} increases almost linearly increasing with frequency. It also increases with temperature at all frequencies. The frequency dependence of σ_{ac} is due to the movement of mobile charge carriers and the polarization effects [29,30,31,32]. The increase of σ_{ac} with temperature is attributed to the impurities, which locate at the grain boundaries. Moreover, the increase may be due to thermally activated charge carrier mobility [32,33,34,35,36,37].

The temperature dependence of ac conductivity can be described by Arrhenius equation given as follows [35,36,37,38,39,40,41],

where σ_{0} and E_{a} represent the pre-exponential factor and the activation energy of mobile charge carriers, respectively. T is the absolute temperature and k_{B} is the Boltzmann constant. Figure 5 shows Arrhenius plots (lnσ_{ac} vs. 1000/T) of ac conductivity at various frequencies. As seen in Fig. 5, for all frequencies, the Arrhenius plots indicate two linear regions which correspond to Region 1 (150–250 K) and Region 2 (300–350 K).

The E_{a} values were determined by finding the slopes of the two linear regions. The obtained E_{a} and σ_{0} values are given in Table 1. As seen in Table 1, the E_{a} value increases with increasing temperature at all frequencies. At low temperatures, the low E_{a} value may be associated with recombination causing more departures from thermionic-emission. Besides, the E_{a} value decreases with increasing frequency in the low temperature range (Region 1), while it increases with increasing frequency in the high temperature range (Region 2).

The total electrical conductivity at a given temperature can be analyzed by Jonscher’s universal power law [42]:

where σ_{dc} represents the dc part of conductivity which is frequency independent, and Aω^{s} represent the ac part of conductivity which is frequency dependent. Thus, the ac conductivity (σ_{ac}) is defined as [41,42,43,44,45,46,47,48],

where A is a pre-factor that depends on temperature and s is the frequency exponent with the range, 0 < s < 1. Also, the s parameter represents the interaction between mobile ions and the surrounding lattice. Figure 6 shows the variation of ac conductivity with frequency at various temperatures. As seen in Fig. 6, for all temperatures, these plots indicate a linear region. The s value is determined from the slope of the linear part. The calculated s values for 150, 200, 250, 300, 325 and 350 K were found to be 0.22, 0.16, 0.12, 0.13, 0.14 and 0.21, respectively. The s values were found as s < 1. This behavior of s with temperature indicates that conduction mechanism may be analyzed by the correlated barrier hopping (CBH). According to the CBH model, the conduction occurs by hopping of charge carriers between localized sites over potential barrier.

## Conclusions

In the present study, the Au/Si_{3}N_{4}/p-GaAs (MOS) capacitor was fabricated. Complex dielectric permittivity (ε*), modulus (M*) and conductivity (σ*) of the MOS capacitor were investigated using temperature and frequency dependent capacitance and conductance measurements. The obtained results confirm that both frequency and temperature changes have significant effects on the electric and dielectric properties of the MOS capacitor. The ε′ and ε″ value decrease with increasing frequency at all temperatures. The change of ε′ and ε″ with frequency is due to mainly space-charge/interfacial and orientation polarizations. The ac electrical conductivity (σ_{ac}) increases as the temperature increases. While the activation energy (E_{a}) value obtained from Arrhenius equation decreases with increasing temperature in Region 1, its value increases with the temperature in Region 2. Besides, the frequency dependence of σ_{ac} at various temperatures is found to obey the power law. Correlated barrier hopping (CBH) was described as the conduction mechanism of charge carriers in the structure.

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## Acknowledgements

This study was supported by Gazi University Scientific Research Project. (Project Number: GU-BAP.05/2019-26).

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Türkay, S., Tataroğlu, A. Complex dielectric permittivity, electric modulus and electrical conductivity analysis of Au/Si_{3}N_{4}/p-GaAs (MOS) capacitor.
*J Mater Sci: Mater Electron* (2021). https://doi.org/10.1007/s10854-021-05349-z

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