Complex dielectric permittivity, electric modulus and electrical conductivity analysis of Au/Si₃N₄/p-GaAs (MOS) capacitor

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 [14‐16].

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 [5‐7, 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 C₀ (= ε₀A/d) is the capacitance of an empty capacitor. ε₀ (= 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 [19‐23]. 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″ [19‐26]. The obtained results for the Au/Si₃N₄/p-GaAs (MOS) capacitor were found to be consistent with those reported in the literature [19‐21]. 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.

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 [25‐31].

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 [29‐32]. 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 [32‐37].

The temperature dependence of ac conductivity can be described by Arrhenius equation given as follows [35‐41],

where σ₀ 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 σ₀ 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 [41‐48],

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.