Impedance Spectroscopy and Dielectric Relaxation of Imidazole-Substituted Palladium(II) Phthalocyanine (ImPdPc) for Organic Solar Cells.

In this study, we investigated the potential of palladium tetrakis (imidazole) phthalocyanine (PdPc(Imz)4) for use as an organic semiconductor for improving the photovoltaic performance. In order to get more information about the prevailing model of the conduction mechanism (correlated barrier hopping (CBH)) for PdPc(Imz)4, electrical impedance measurements were performed at different temperatures and the obtained data were simulated by the Kohlraush Williams Watt (KWW) approach. Theoretical studies (density functional theory (DFT)) were performed and molecular electrostatic potential (MEP) maps were also extracted to understand the relationship between the molecular structures and the molecular electronic structure of PdPc(Imz)4 and its semiconductor properties. Furthermore, studies on the AC electrical process as a function of temperature highlighted a hopping charge transport according to an equivalent electrical circuit composed of a parallel constant-phase element (CPE), capacitance in the grain boundary layer (C g), and resistance of the grain boundary (R g). To improve interpretation of the results, an in-depth analysis of the behavior of the electric transport was conducted. As a result, the correlated barrier hopping (CBH) conduction mechanism was shown to be the most suitable predominant conduction mechanism.

Introduction

In recent years, the application of organic semiconductors in microelectronics technologies has gained a new impetus due to the growing demand for low- and high-dielectric-constant materials.

Numerous reviews and articles address various aspects of the emerging semiconductor field enabling future innovations in optoelectronic devices. Some focus on the intrinsic properties of the materials, while others highlight applications such as photovoltaic cells, light-emitting diodes, and transparent transistors. Compared to these large families of materials, chalcogen-based wide-band-gap semiconductors (Ch = S, Se, Te) (Eg > 2 eV) are characterized by their propensity for p-type doping, high mobility, high valence-band positions, and lower ionization energies.[1−5] However, compared to M–O bonds, the weaker M–Ch (with Ch = S, Se, Te) bonds in these materials may lead to increased degradation and stability concerns in chalcogenides.[6]

Despite most of the research studies being focused on wide-band-gap inorganic materials, semiconductors are not limited to oxides and chalcogenides. Recently, several classes of organic semiconductors have been shown to have a great potential in the field of electronics and photoelectronics.

Organic semiconductors have emerged as an attractive technological alternative for large-scale power generation instead of the classic inorganic solar-cell technologies. In addition, while most inorganic solar panels require high-purity crystalline substrates, phthalocyanine-based organic solar cells (OSCs) are inexpensive, light, and can be built on a large area, without the concern of strain-induced defects.[7] Since the discovery of the semiconducting property of phthalocyanines (Pc),[7] these compounds have become one among the most used products for solar cells.[8−10]

Metallophthalocyanines (MPcs) with a lower band gap that have been widely used as electron donor material show reasonable ambipolar carrier-transporting properties for efficient charge transfer. Moreover, these compounds have been reported to be among the promising electron acceptor materials in organic solar cells (OSCs).[11]

Organic photovoltaic devices are a combination of electron donor and acceptor materials, at the interface of which a dissociation of excitons occurs (bound electron–hole pairs, formed by the absorption of a photon in the organic layer).[12] The small, macrocyclic, aromatic-copper phthalocyanine molecule (CuPc) has been shown to be a good donor layer for photovoltaic devices when combined with fullerene (C60) as an acceptor material.[13] This architecture integrated the advantages of both the Schottky barrier and the donor–acceptor heterojunction in photovoltaic cells. Indeed, the Schottky barrier can provide a high Voc and the donor–acceptor heterojunction can provide more dissociation sites, which allows obtaining more photocurrent.[14]

Many studies on the modified phthalocyanine with various central metal atoms and chemical substitution have been at the focus of multidisciplinary interests ranging from photodynamic therapy in cancer treatment[15] to pigments such as the blue- and green-color filters of liquid crystal displays (LCDs),[16] and as organic thin-film transistors (OTFTs).[17] Moreover, phthalocyanines offer tremendous possibilities for the development of field-effected transistors whose charge carrier mobility greatly exceeds 1 cm2 V–1 s–1,[18] an improvement in the power conversion efficiency of the solar cell larger than 5%,[19] and also for pollution monitoring as smart sensors.[20] Consequently, significant interest has been generated for the study of the electrical properties of Pc compounds and their derivatives. Khalil et al.[21] have deposited 4-tetra-4-tolylsulfonyl:zinc phthalocyanine (4T4TS:ZnPc) thin films by the spin coating technique on quartz substrates. The authors reported that the X-ray diffraction (XRD) spectra of 4T4TS:ZnPc showed a monoclinic crystalline structure in phase with a preferential orientation along (002) and (1̅02). Indeed, in view of their efficient use in different applications, the study of the dielectric relaxation process and the electrical conductivity of these compounds has been greatly solicited. Some of the dielectric properties of PdPcs have been reported.[22−25]

In previous studies, we characterized PdPc and its derivatives deposited in the form of thin layers by vacuum evaporation and obtained encouraging results.[26−28] However, there is insufficient literature regarding the study of imidazole PdPc.

In the present paper, we report the study of the potentiality of palladium tetrakis (imidazole) phthalocyanine (PdPc(Imz)4) as a donor material for new applications in electronic and photoelectronic components in solar cells. The dielectric relaxation of PdPc(Imz)4 has been studied using temperature-varied complex impedance spectroscopy and the conduction mechanism has been examined by AC and DC conductivity.

Results and Discussion

Theoretical Results of PdPc(Imz)4

To give more information about the electronic features of the optimized PdPc(Imz)4 compound, the electronic density plots of molecular orbitals are presented in Figure . In addition, ELUMO, EHOMO, and EHOMO–4 energy values of the PdPc(Imz)4 compound were also calculated. In the orbits of the palladium phthalocyanine molecule, the calculated values were ELUMO = –3.2745 eV, EHOMO = −5.5381 eV, and EHOMO–4 = −6.822 eV.

Figure 1

Theoretical analysis of PdPc(Imz)4. (a) Geometry-optimized molecular model. (b) Calculated density of states (DS) for the model.

In order to get an idea of the molecular stability, the chemical hardness (η) of PdPc(Imz)4 was calculated by determination of the highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) energies.[29,30] To enhance the efficiency of the dye-sensitized solar cells (DSSCs), there is a need to understand the molecular behavior of PdPc(Imz)4 under an electric field.[31] The global chemical reactivity descriptors of PdPc(Imz)4, such as the potential (μ), the chemical hardness (η), the electronegativity (χ), and the electrophilicity power (ω) were deduced from the HOMO and LUMO energies (see Table ).[32]

Table 1

Calculated HOMO, LUMO, Energy Gap (Δ), and Global Chemical Reactivity Descriptors

molecules’ energy	6-311G
ELUMO	–3.2749
EHOMO	–5.5381
energy gap (Δ) EHOMO – ELUMO	2.2632
ionization potential (IP= −EHOMO)	5.5381
electron affinity (EA = −ELUMO)	3.2749
chemical hardness (η = (I – A)/2)	1.1316
chemical softness (s = 1/2η)	0.5658
chemical potential (μ = (I + A)/2)	4.4065
electronegativity (χ = (1 + A)/2)	2.1374
electrophilicity index (ω = μ2/2η)	10.9862

Table illustrates the calculated values of the highest occupied molecular orbital energy EHOMO, the lowest unoccupied molecular orbital energy ELUMO, and the energy gap Egap (in eV) of PdPc(Imz)4. From our calculations, the Egap in which the PdPc(Imz)4 shows semiconductor behavior is 2.263 eV. The calculated values of the ionization potential (IP) and the electron affinity (EA) showed that PdPc(Imz)4 has a very high ability for donating or accepting an electron and becoming a cation or an anion. These values are related to the low value of the energy gap (Egap = 2.263 eV) of the compound and indicates a semiconductor behavior. Considering that there is a correlation between band gaps and bond energies, and that electronegativities come from bond energies, we may expect a correlation between the band gaps and electronegativity. Among the global descriptors of chemical reactivity, electronegativity is often used to predict the manner and direction in which materials will transport energy/electricity/heat. In addition, the value of the electrophilicity index (ω) suggests that the maximum flow of electrons between the donor and the acceptor is quite large. Furthermore, since the ionization potential of PdPc(Imz)4 is 5.53 eV (Table ) and given the Ag work function (4.35 eV),[33] we may assume the presence of a small energy barrier (SEB) of 0.18 eV at the Ag/(PdPc(Imz)4) interface, which is less than 0.3 eV, indicating that the transport current is due to the charge-limited currents (SCL).

The photochemical and photophysical properties of phthalocyanines depend on both central metal atoms and peripheral substitutes. The planar molecules are arranged with their planes parallel to the substrate surface. From Figure , we can see that there are several energies relating to the critical number of electrons corresponding to the isosurface distribution for LUMO and HOMO. The activation energy of the PdPc(Imz)4 compound can be deduced from the energy difference between the Fermi level and the previous peak corresponding to the greatest number of electrons.[34] As shown in Figure , this value is estimated to be 0.36 eV.

Figure 2

Isosurface distribution plot for LUMO, HOMO, and the next molecular orbital, with their corresponding energies.

In this study, molecular electrostatic potential (MEP) maps were extracted with SDD basic sets. The MEP plot of PdPc(Imz)4 is characterized by a positive region (blue) at its center around the palladium atom (Figure a), indicating that this region is responsible for the repulsion of the proton by the atomic nuclei. The major negative region (between light brown and yellow) located on the nitrogen of the isoindole and imidazole parts of the PdPc(Imz)4 compound indicates the minimum electrostatic potential (which means that there is an excess of electrons). The color ranges (in kcal/mol) from red (−4.238 × 10–2) to blue (+4.238 × 10–2).

Figure 3

Electron density of PdPc(Imz)4 compounds from the total SCF density (isoval = 0.025, mapped with the electrostatic potential (ESP)).

As shown in Figure b, the outer contour around the core is the lower isosurface and the positive charges are distributed on the exterior parts of the ligands. Since ESP highlights the negative and positive regions of a molecule, it can be said that the analysis of the electron density of PdPc(Imz)4 allows us to understand the observed modifications of the electronic properties.

The electron density contours (Figure ) show noticeable differences in the electron distribution, indicating that the core of ImPcz is the form responsible for the protonic electric conductance.

Electrical and Dielectric Properties of the PdPc(Imz)4 Compound

Complex Impedance Analysis

To determine the parameters of the equivalent circuit corresponding to the PdPc(Imz)4 compound, we performed a deconvolution of the Z′ and Z″ curves as a function of the frequency. The simulation of the experimental data was carried out using the least-squares method based on eqs and 3. The adjustment parameters were Rp, Q and α. The approximate values of the adjustable parameters were obtained as follows: Rp is the limit of Z at low frequencies and is deduced from the intersection of the representative circle of Z with the axis of the real parts on the side of the large values of Z; Q is calculated from the maximum value of Z′ as a function of the frequency; α = (1 – α)π/2 is the angle of inclination of the segment, which passes through the origin of the reference frame and the end of the circular arc at a low frequency.

Figure shows the plots of the angular frequency dependence of the impedance real part of PdPc(Imz)4 at different temperatures. The amplitude of the real part Z′ is higher in the region of angular frequencies <4 × 106 Hz, and decreases with increasing frequency until it becomes constant at all temperatures. Furthermore, the amplitude of the real part of impedance (Z′) increases with the increasing temperature and shifts to the high-frequency side, suggesting the presence of space charge polarization in the PdPc(Imz)4.[35,36] The same behavior of Z′ has been previously noticed in many other phthalocyanine materials.[37] The observed temperature dependence of the actual impedance Z′ may be a factor responsible for the improvement of the AC conductivity of the material with temperature at higher frequencies.[38]

Figure 4

Variation of the real part of the impedance as a function of the angular frequency at various temperatures.

Figure depicts the angular frequency dependence of the impedance imaginary part Z″ of PdPc(Imz)4 at various temperatures. It shows that the amplitude of Z″ increases until reaching a maximum peak (Zmax″), and afterward, it decreases with the increasing temperature in the same way as the frequency. The shift in the peak position corresponding to the maximum frequencies goes along with the asymmetric broadening of the loss peaks, indicating the existence of a temperature-dependent electrical relaxation phenomenon with the spread of relaxation times.[39] It is worth mentioning that the decrease of the magnitude of the imaginary impedance with the increase of the temperature, as well as the merging of all of the curves at high frequencies, indicates a possible release of the spatial charge in the material.

Figure 5

Variation of the imaginary part of the impedance as a function of the frequency at various temperatures.

Figure highlights a particular point of frequency around which Z″ has a maximum value and where it intersects with Z′. Moreover, when increasing the temperature from 503 to 538 K, the frequency corresponding to Zmax″ continues to shift upward gradually from 4.058 × 106 Hz to reach 5.86 × 106 Hz. The obtained results reveal that this physical phenomenon is further evidence for the relaxation time distributions arising from the molecular structure of PdPc(Imz)4.

Figure 6

Frequency dependence of Z′ and Z″ for PdPc(Imz)4 at various temperatures.

Equivalent Circuit

As shown in Figure , the imaginary part of the impedance Z plotted vs its real part Z at several measurement temperatures in the range 503–553 K generates depressed semicircles. Furthermore, the decreasing radius of the arcs, which become gradually more circular with increase in the temperature, demonstrates the semiconducting nature of the phthalocyanine.[34] Most of the authors attribute this phenomenon to the Debye relaxation behavior of the grain boundaries[38] due to the nonhomogeneity of the grains, to the variations among the grain boundaries combined in series/parallel connection, and to the measured response of each individual grain boundary.

Figure 7

Cole–Cole diagrams of PdPc(Imz)4 for a range of temperatures.

Modeling the measured impedance spectra can allow us to build an idea about the electrical equivalent circuit as well as the electrical phenomena inside the PdPc(Imz)4 structure. A full semicircle with its center lying on the axis of the real part of the complex plane can be expressed in terms of a simple parallel RC equivalent circuit. In order to determine if the deviation from the ideal capacitive behavior is due to the nonhomogeneity of some properties of the system, a new constant-phase element (CPE) is introduced into the equivalent electrical circuit in place of the ideal capacitance. The explanation for the significance of the constant-phase element (CPE) has been widely discussed by Pajkossy[40] and Córdoba-Torres et al.[41] Several programming methods for computing the circuit parameters are available in the literature.[42,43] In this study, we used the Z-view (II) software commonly utilized for analyzing and computing electrical circuits.

The program was run over 100–500 iterations with different CPE exponents to improve the goodness of fit and get the maximum fitting. The results indicate that our data are best modeled as an active CPE circuit involving three components connected in parallel (Figure ). The fitting parameters of the equivalent circuit at different temperatures are given in Table . In this study, the model of the equivalent electrical circuit obtained differs from the one proposed by Oruç et al.[39] (RC parallel circuits in series with CPEs) for phthalocyanine deposited on pure indium electrode using the thermal evaporation technique. This difference can be explained by the reduction of grain boundaries and crystalline bulk in the case of phthalocyanine in thin-film form, which reduces the resistance of the grain boundary. In the model proposed by Oruç̧ et al.[39], the non-Debye relaxation behavior may have originated from the joints between grains, where Cg represents the capacitance of the grain boundary region.[44,45]

Figure 8

Cole–Cole plots at a temperature of 523 K with an electrical equivalent circuit.

Table 2

Values of the Parameters of the Equivalent Circuit at Different Temperatures

T (k)	Rg (Ω)	Q (Ω–1sα)	α	Cg (F)
503	6.25 × 106	2.3 × 10–6	0.76	2.5 × 10–7
508	5.43 × 106	2.0 × 10–6	0.76	2.3 × 10–7
513	4.48 × 106	2.2 × 10–6	0.75	2.8 × 10–7
518	3.96 × 106	2.0 × 10–6	0.75	2.0 × 10–7
523	3.56 × 106	2.2 × 10–6	0.76	2.0 × 10–7
528	3.10 × 106	2.0 × 10–6	0.76	2.1 × 10–7
533	2.83 × 106	1.8 × 10–6	0.73	1.9 × 10–7
538	2.68 × 106	2.0 × 10–6	0.75	2.0 × 10–7
543	2.78 × 106	1.8 × 10–6	0.75	2.2 × 10–7
548	2.21 × 106	2.0 × 10–6	0.74	2.1 × 10–7
553	1.89 × 106	1.8 × 10–6	0.73	2.0 × 10–7

The impedance of the constant-phase element (CPE) is given by the relationshipwhere the term Q [Ω–1sα] represents the CPE magnitude, ω (ω = 2πf, f being the frequency) signifies the angular frequency, and j2 = −1 is the imaginary number. The parameter α is related to the phase shift Φ = −α(π/2) degrees, which is independent of the frequency.

The whole parameters of the impedance of the constant-phase element (CPE) have been evaluated by Z-view fitting according to the following equationsThe electrical conductivity σDC was calculated as followswhere e and S represent the thickness and the area of the sample, respectively. The bulk ohmic resistance Z0 is deduced from the complex impedance diagrams (Figure ).

Figure depicts the thermal effect on the conductivity DC, ln(σDCT), against the reciprocal temperature according to the equation governed by the Arrehenius lawwhere σDC is the DC conductivity, A is the pre-exponential factor, T is the absolute temperature, Ea is the apparent activation energy for the mobile ions, and kβ is the Boltzmann’s constant. The activation energy deduced from the slope of the curve (Figure ) is 0.59 eV.

Figure 9

Variation of ln(σDCT) vs 1000/T.

Electric Modulus Study

In order to study in more detail the conduction process and/or relaxation of PdPc(Imz)4, the representation of the electric modulus M* is very useful to describe the electric conduction mechanism.

The complex electric modulus, M*, is described in terms of the inverse of the complex permittivity ε* as followsThe real M′ and imaginary M″ parts of M* have been calculated using the following relationsThe angular frequency dependence of M′ and M″ at different temperatures for PdPc(Imz)4 pellet are depicted in Figure a,b.

Figure 10

Frequency dependence of (a) M″ and (b) M′ at different temperatures.

The value of the real part of the dielectric modulus M′ is very small in the region of angular frequencies ≤4 × 106 Hz, but increases with increasing angular frequency at all temperatures. This tendency may be explained by the inability of the restoring force to conduct charge carrier flow to their equilibrium position under the influence of a constant electric field.[46] Instead, in the imaginary part of the electric modulus M″, there appears a broad peak that shifts toward a higher angular frequency ωmax (=2πfmax) up to a maximum peak, Mmax″, then decreases as the temperature increases (Figure a). The broad shapes of the asymmetric peaks may be attributed to the phenomenon of a relaxation time distribution,[47] revealing the correlation between the motions and the mobile charge carriers.[48] Therefore, the profile of the modulus spectra confirms the existence of the hopping mechanism in the electrical conduction of the PdPc(Imz)4 materials. On the other hand, the charge carrier mobility is governed by the thermally activated hopping within the localized states of the energy distribution (HOMO or LUMO) of the polypyrrole.[49] The circuit shown in Figure representing a parallel combination of a resistance (Rg), a capacitance (Cg), and a fractal capacitance (CPE) confirmed the phenomenon of the relaxation time distribution in PdPc(Imz)4 pellet.

The angular frequency ωmax, corresponding to Mmax″, gives the relaxation times, τM[47]In addition, the shifts in the peak frequencies toward higher values with increase in the temperature is a consequence of the hopping transport. The calculated average relaxation time from Figure a was 1.82 × 10–8 s. For a further investigation, the temperature variation of the relaxation time τmax at the maximum of M″ was studied (Figure ) using the Arrhenius equationwhere τ0 is the pre-exponential factor and ΔEω is the activation energy for the electric modulus (≈0.32 eV). The observed value for the activation energy is comparable to that reported by Soliman et al.[50] for aluminum phthalocyanine chloride (AlPcCl). The authors reported an activation energy ΔEω = 0.34 eV.

Figure 11

Arrhenius plot of the relaxation-time τmax spectra.

From Figure , it can be seen that the activation energy calculated from the Arrhenius relation is ΔEw = 0.32 eV. The magnitude of the activation energy suggests that the carrier transport exhibits a typical hopping conduction. Furthermore, all of the curves in Figure a show an asymmetric peak at the higher-frequency side. This behavior can be interpreted using Kohlraush Williams Watt (KWW) decay function, which describes the degree of deviation from the relaxation of a single charge carrier in the time domain.[51]

The complex electric modulus, M*, against log ω plots for a certain number of ion-conducting materials is well interpreted by the Laplace transformwhere the exponent β (0 < β < 1) describes the degree of non-Debye behavior, is the inverse of the dielectric constant, and τKWW represents the relaxation time of the KWW function. A new fitting approach proposed by Bergman allows a direct analysis of the frequency domain.[52] The imaginary parts M″(ω) can be written after approximation asIn this study, the experimental data are fitted using the modified KWW approach. The variation of the imaginary part of the normalized modulus (M″/Mmax″) as a function of ω/ωmax at different temperatures is depicted in Figure .

Figure 12

Frequency dependence of the normalized peaks M″/Mmax″ for the PdPc(Imz)4 pellet at different temperatures.

An overlapping of the peak positions of the M″(ω)/M″ is observed, suggesting components from both long range and localized relaxation. In this study, the Gaussian fitting of the normalized modulus peaks (Figure ) gives a value of full width at half height (FWHH) equal to 1.78 decades (Kohlrausch parameter β = 0.64 = 1.14/FWHH). Consequently, the FWHH value is greater than the FWHH for the Debye relaxation (1.14 decades), which confirms that this relaxation follows a non-Debye-type behavior.[47]

Figure 13

Gaussian fitting of the normalized modulus peaks at 503 K.

Frequency and Temperature Dependence of AC Conductivity

The AC conductivity response of phthalocyanine has been thoroughly investigated to understand the distribution of the electric field intensity and the perturbations driven once the system is subjected to an electric field.[28,53] In this study, the AC conductivity properties and charge transport mechanism were studied on the PdPc(Imz)4 pellet in the frequency and temperature ranges of 1–10 MHz and 503–553 K, respectively (Figure ). The AC electrical conductivity can be computed in accordance with the empirical relationwhere Z′ and Z″ are, respectively, the real and the imaginary parts of the complex impedance, and e and σ represent, respectively, the thickness and the area of the pellet.

Figure 14

Frequency dependence of AC conductivity at various temperatures for the PdPc(Imz)4 pellet.

The behavior of the total conductivity dispersion has been introduced and analyzed by Jonscher as follows[47,54,55]The equation reflects two different conduction mechanisms, represented by σdc and ω, where σdc is the DC conductivity (ω = 0 rad s–1), A is the temperature-dependent parameter, and s is the fractional component varying between 0 and 1, characterizing the deviation from Debye behavior in the molecular system. The s values were calculated from the slope of the straight portions of the σac vs frequency plot. A defines the strength of polarizability. The values for the exponent factor s were determined from eq and the σac (ω) vs frequency plot (Figure ).

The variation of the AC conductivity of the PdPc(Imz)4 pellet (Figure ) shows two distinct regions (regions I and II). These regions are referred as I (f < ∼4 × 106 Hz), which exhibits a conductivity-independent frequency (DC conductivity region), and II (f > ∼4 × 106 Hz), which is related to strong frequencies.

Figure 15

Plots of log σ(Ω–1 cm–1) vs 1000/T at different frequencies for PdPc(Imz)4.

In region I, where the DC-conductivity plateau at angular frequency is less than 4.0 × 106 Hz, the electric field is not sufficient to perturb the charge carriers. As a result, the value of the conductivity remains nearly constant. In region II, the angular frequency is greater than 4.0 × 106 Hz. This region is known as the dispersive Jonscher’s region, where the exponent values are between 0 and 1 (s < 1). This behavior may be expected to be due to the translational hopping motion of the charge carriers in the material.[56,57] The fitting parameters extracted using Jonscher’s power law are summarized in Table .

Table 3

Values of the DC Conductance, the Constant (A), and the Exponent (s) for PdPc(Imz)4

T (K)	σdc (Ω–1 cm–1)	A	exponent s
503	7.64 × 10–6	6.19 × 10–11	0.98
508	8.65 × 10–6	4.51 × 10–11	0.97
513	1.19 × 10–5	2.91 × 10–11	0.96
518	1.25 × 10–5	1.75 × 10–11	0.80
523	1.36 × 10–5	1.19 × 10–11	0.75
528	1.53 × 10–5	9.53 × 10–11	0.66
533	1.66 × 10–5	9.56 × 10–12	0.61
538	1.69 × 10–5	8.17 × 10–12	0.55

These results are in good agreement with those reported in other studies, in which several metallophthalocyanine-based materials were used, such as CoPc (s = 0.7–0.8),[58] MoPc (s = 0.9),[59] MgPc (s = 0.71–0.99),[60] and Ni–Pc(COOH)8 (s = 0.42–0.67).[38]

The variation of AC conductivity (ln(σAC)) as a function of temperature at three different frequencies is depicted in Figure . It can be seen that the conductivity of the PdPc(Imz)4 pellet increases with increasing frequency and temperature. In addition, we can notice that Ea decreases with increasing frequency. This behavior reveals that the applied field frequency favors the electronic hopping between the localized states and consequently, the increase in AC conductivity.[61,62]

The temperature dependence of the exponent factor (s) for values less than unity is attributed to the short-distance charge hopping between the localized states. Various theoretical models for hopping were suggested under the applied AC field to elucidate the conduction mechanisms in materials, such as the quantum mechanical tunneling (QMT) model,[63] the correlated barrier hopping (CBH),[64,65] the nonoverlapping small polarons (NSPT) model,[66] and the overlapping large polaron tunneling (OLPT) model.[28,53] The temperature dependence of the extracted (s) values for the Ag/PdPc(Imz)4/Ag structure is shown in Figure . Among the proposed models, the present study showed that the exponent (s) values decrease with the increase of temperature and σac increases with the increasing frequency (Figure ). Therefore, the correlated barrier hopping (CBH) model[65,67] was adopted to characterize the electrical conduction mechanism of PdPc(Imz)4. For this model, WM = 0.27 eV (Figure ). According to the CBH model, the binding energy prediction is given by the following equation[67,68]where τ0 is the characteristic relaxation time (in the order of the atom vibrational period = 10–13 s);[65]WM is the binding energy; kB is Boltzmann’s constant; and ω is the angular frequency.

Figure 16

Thermal variation of the exponent s of PdPc(Imz)4.

In Figure , the experimental data for frequency exponent s are fitted with the predictions of the CBH model using eq , and the fit of the s-curve is used to determine the value of the binding energy WM of the carrier in its localized sites. At 503 ≤ T ≤ 538 and f ≥ 6 × 106 Hz, the frequency exponent is close to unity. Therefore, S → 1 with the increase in frequency and with the small values of . On the other hand, S → 0 in the frequency range less than 6 × 106 Hz and became effectively independent of temperature. It can be pointed out that the most suitable conduction mechanism can be considered as a multiple-jumps mechanism in the frequency range f < 2 × 106 Hz (low s values) and as single jumps for f > 2 × 106 Hz (high s values) for the studied PdPc(Imz)4 pellet. The same orders of s magnitude, corresponding to the same type of temperature dependence, have been reported by other authors for different phthalocyanine films.[69,70]

The frequency dependence of the total electrical conductivity σac at different temperatures of the PdPc(Imz)4 pellet is shown in Figure . From the above-mentioned results, regarding the variation of s in relation to the temperature and of the total electrical conductivity σac in relation to frequency, we may infer that the hopping model is the most appropriate for the PdPc(Imz)4 material under an electric field.

Dependence of Dielectric Constant (ε′) and Loss Spectrum (ε″) on the Angular Frequency and Temperature

Most materials referred to as dielectrics exhibit three kinds of polarization, namely electronic polarization, atomic (or ionic) polarization, and orientational polarization. Nevertheless, the distortion polarization results from electronic and atomic polarization.[71,72]Figures and 18 depict the frequency dependence of the dielectric constant (ε′) and dielectric loss (ε″) of the PdPc(Imz)4 pellet at different temperatures.

Figure 17

Dielectric constant spectra of the PdPc(Imz)4 pellet at different temperatures.

Figure 18

Dielectric loss spectra of the PdPc(Imz)4 pellet at different temperatures.

The graphical plot of the real part (ε′) of the complex dielectric permittivity vs angular frequency (ω) exhibits two regions. At an angular frequency of less than 4 × 107 rds–1, ε′ increases as ω decreases with a rapid increase at high temperatures, in agreement with the results of dielectric measurements reported for zinc and copper phthalocyanine.[73,74] On the other hand, for angular frequencies greater than 4 × 107 rds–1, as the frequencies increase, the dielectric values decrease before becoming constant at ∼3.4, which is the intrinsic dielectric constant of PdPc(Imz)4. This phenomenon of decrease of the dielectric value is known as the anomalous dielectric dispersion. The dielectric constant increases as the temperature increases, which is attributed to the blocking of charge carriers at the electrodes.[73] At an angular frequency of less than 4 × 107 rds–1, the same behavior was observed for ε″, which can be attributed to the contributions of the deformation and the relaxation polarization.[75] Afterward, as the frequency is increased, the value of ε″ becomes constant when reaching ∼3.04. These phenomena can be explained by the strong attenuation of the rotational polarization of the molecular dipoles of PdPc(Imz)4 when the frequency is increased under the effect of the electric field. Hence, the dipole orientation slows down the AC electric field due to the contribution of the deformation polarization.[75] The spectacular decrease in ε″ was widely researched for potential applications of these dielectric materials in electrical energy storage.[76−78]

Conclusions

In this work, a sandwiched pressed pellet of palladium tetrakis(imidazole) phthalocyanine (PdPc(Imz)4), Ag/(PdPc(Imz)4)/Ag, was characterized by impedance spectroscopy. The SCF density shows a noticeable difference of electron distribution, suggesting that the core of ImPcz is the form responsible for the protonic electric conductance. The complex plane plots of the impedance Z at several measurement temperatures ranging from 503 to 553 K generated depressed semicircles with different radii, indicating the semiconductor property. The depressed arcs simulation of the complex Z″ as a function of the Z′ plane plots indicated that the model of the equivalent circuit can be represented as a parallel combination of RC and CPE. The relaxation phenomenon has been also confirmed by the Kohlraush Williams Watt (KWW) approach. Moreover, the prevailing conduction mechanism in the PdPc(Imz)4 pellet, under an AC field, can be successfully attributed to the correlated barrier hopping (CBH) model. The slope of the Arrhenius plot was determined to find the activation energy (0.56 eV). These results indicate that PdPc(Imz)4 might be used as an active layer in the design of solar cells.

Experimental Section

Material’s Synthesis

Palladium(II) tetrakis (imidazole) phthalocyanine (PdPc(Imz)4) was synthesized from 4-(1H-imidazol-1-yl)phthalonitrile and palladium(II) acetate, in the presence of the catalyst 1,8-diazabicyclo[5.4.0]undec-7-ene (DBU) as described in previous papers.[26,27] The synthesis route is shown in Figure .

Figure 19

Palladium(II) phthalocyanine tetra-imidazole (PdPc(Imz)4) synthesis.

Electrical Measurements

The electrical measurements were performed on the PdPc(Imz)4 powder at room temperature under ∼2900 bar by means of an hydraulic press. The pellets were obtained in the form of circular discs that were 8 mm in diameter and 2.3 mm in thickness and were painted on both sides with a conductive silver paste to behave as ohmic contacts. The complex impedance measurements were performed by a TEGAM 3550 impedance analyzer monitored by a microcomputer in the frequency range 1–10 MHz. Complex impedance measurements were carried out over the temperature range 503–553 K. The temperature was controlled using a thermocouple with 2° precision placed near the sample. The measurement results are given by the representation of the imaginary part, according to the real part of the complex impedance.[79] The software package Z-view was used to improve the goodness of fit and to compute the electric circuit parameters of the system.

Computational Details

Theoretical calculations of the molecular structure of PdPc(Imz)4 were carried out with the density functional theory (DFT)[79] calculations using Gaussian 09[80] and Gaussian view 5.08 programs.[81] The B3LYP-GD3 hybrid density functional method has been applied to improve the description of the ground energetic state of PdPc(Imz)4[82−84] using Stuttgart Dresden double ζ-effective-core potential (SDD ζ-ECPs) basis sets.[85]