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Electric Conduction Mechanisms Study within Zr Doped Mn3O4 Hausmannite Thin Films through an Oxidation Process in Air

L. Ben Said1,2,*, R. Boughalmi1, A. Inoubli3, and M. Amlouk1,2

1Unit of Physics of Semiconductor Devices, Faculty of Science of Tunis, Tunis El Manar University, Tunis 2092, Tunisia, 2Faculty of Science of Bizerte, Carthage University, Zarzouna 7021, Tunisia, 3Laboratory of Physics of Lamellar and Nanomaterial Materials, Hybrids (LPMLNMH), Faculty of Science of Bizerte, Carthage University, Zarzouna 7021, Tunisia
Correspondence to: Said LB, Tel: +216-58-147-883, E-mail: bensaidlilia@gmail.com
Received September 8, 2017; Accepted September 12, 2017.
Abstract

In this work further optical and electrical investigations of pure and Zr doped Mn3O4 (from 0 up to 20 at.%) thin films as a function of frequency. First, the refractive index, the extinction coefficient and the dielectric constants in terms of Zr content are reached from transmittance and reflectance data. The dispersion of the refractive index is discussed by means of Cauchy model and Wemple and DiDomenico single oscillator models. By exploiting these results, it was possible to estimate the plasma pulse ωp, the relaxation time τ and the dielectric constant ɛ. Second, we have performed original ac and dc conductivity studies inspired from Jonscher model and Arrhenius law. These studies helped establishing significant correlation between temperature, activation energy and Zr content. From the spectroscopy impedance analysis, we investigated the frequency relaxation phenomenon and hopping mechanisms of such thin films. Moreover, a special emphasis has been putted on the effect of the oxidation in air of hausmannite thin films to form Mn2O3 ones at 350°C. This intrigue phenomenon which occurred at such temperature is discussed along with this electrical study. Finally, all results have been discussed in terms of the thermal activation energies which were determined with two methods for both undoped and Zr doped Mn3O4 thin films in two temperature ranges.

Keywords : Mn3O4, Zr doping, Thin films, Impedance spectroscopy, Oxidation
INTRODUCTION

MATERIALS AND METHODS

### Films Preparation

Zirconium doped manganese oxide thin films (Mn3O4:Zr)were deposited onto the glass substrates by the spray pyrolysis technique at350°C using 0.1 M Manganese chloride (MnCl2_ 6H2O) solution dissolved in 100 mL of deionized water. To thisstarting solution, we added (ZrCl4_6H2O)as doping agent at various [Zr]/[Mn] molarratios: 3, 6, 12, and 20 at.%. The resulting solution was sprayed at arate flow of 4 mL/min using nitrogen gas. The distance between nozzle andsubstrate was about 27 cm. After the deposition, the samples were allowed tocool slowly to room temperature.

### Characterization Technique

The electrical properties of real and imaginary components of impedance parameters (Z′ and Z″) were obtained using a Hewlett–Packard 4192 analyzer over a wide range of temperature (320°C~450°C) and frequency (5 Hz~13 MHz). Metallic electrodes were painted on the two extremities of the sample using silver paste. The ac conductivity is calculated using the relation: σac=d/Z′A,where Z′, d and A are respectively real part of impedance, distancebetween electrodes and cross-sectional area as displayed in Fig. 1.

RESULTS AND DISCUSSION

### Optical Dispersion of Undoped and Zr Doped Mn3O4

Optical constants by optical dispersion models

The study of the dispersion of incident photon energy plays an important role in the investigation of the optical properties of a material. Fig. 2 shows the refractive index n (λ) and the extinction coefficient k (λ) spectra of undoped and Zr doped Mn3O4 thin films. The extinction coefficient k spectrum shows an obvious decrease versus wavelength and reaches the lowest values in the visible and near infrared ranges which attests the transparency property of Mn3O4 thin films. In the wavelength ranging from 300 nm to 700 nm, the refractive index is found to decrease with the wavelength which represents a normal dispersion. Two approaches could be taken to model this behavior. The first is based on the Cauchy dispersion model and the second used Wemple and DiDomenico single-oscillator one. These two models will be detailed below. However, it is observed that the refractive index increases in 700~1,300 nm domain indicating the existence of an absorption zone where the dispersion is abnormal corresponding well to the gap energy. It is also found that in this zone the dispersion decreases significantly after doping, especially for 3 at.% Zr doped Mn3O4 film. This may be due to the formation of segregated ZrO2 which inhibits the displacement of free carriers. Over the wavelength range λ>1,300 nm, the dispersion becomes normal again which may be due to the inertia of the asperities related to ZrOx oxides. Following zirconium doping, the appearance of another absorption zone above 2,000 nm for both 3 at.% and 6 at.% Zr doped Mn3O4 samples is also depicted which could be attributed to the appearance of a new Zr level in the band gap energy. This decrease regarding the refractive index n and the extinction coefficient k values after doping are detected suggesting an optical windows application of the Zr doped Mn3O4 thin films as previously shown via photoluminescence study (Said et al., 2017).Outside these absorption zones, since the films are optically transparent in thevisible range and for photons energies below the band gap energy (E<Eg),the refractive index n (λ) could be modeled according to Cauchydispersion expression:

$n (λ)=A+Bλ2$

where A and B are Cauchy parameters and the unit of wavelength is μm. The variations of n as a function of λ2 are displayed in Fig. 3. The final values of A and B were determined by fitting the model-generated data to the experimental ones and are gathered in Table 1. In the same zone (i.e., in the visible spectral range as shown in the inset of Fig. 2), in addition to the Cauchy model, the curves n (λ) below the inter-band absorption edge shows a Sellmeier dispersion type dependence as reported in literature (Mardare & Hones, 1999)and could be thus studied by means of the Wemple and DiDomenicosingle-oscillator model to investigate the average excitation energy E0 and dispersion energy Ed of the deposited material (DiDomenico et al., 1969; Wemple & DiDomenico, 1971). According to this model, the refractive index is related to the energy of the incident photons by the following expression:

$1n2-1=E02-(hv)2E0Ed$

where E0 and Ed are the single-oscillator energy and dispersion energy parameter, respectively. By using relation (2) in the following form:

$1n2-1=E0Ed-(hv)2E0Ed$

We can plotted (n2−1)−1 vs. (hν)2 for different doping levels and the values of E0 and Ed are directly determined from the slope of (E0Ed)−1 curves and the intercept of (E0/Ed) on the vertical axis, Fig. 4. These values are gathered in Table 1. In the literature, the dispersion parameters of several materials were investigated based on this model (Caglara et al., 2007; Mrabet et al., 2015; Ouni et al., 2010; Park, 2012). As expected, Ed value decreases with Zr content leading to an increase of the optical dispersion phenomenon.

Optical dielectric characterization and optical conductivity

The complex dielectric constant ɛ (λ) characterizes the optical properties of a solid material. Using n and k calculated data, the dielectric constants are deduced from the following system:

${ɛ1(λ)=n2(λ)-k2(λ)ɛ2(λ)=2n(λ) k(λ)$

The variations of ɛ1(λ) and ɛ2(λ) are given in Fig. 5. In the near infrared region, when n2 is higher than k2, and ωτ<<1, the real andimaginary parts of the dielectric constant can be expressed by the followingrelations (Belgacem & Bennaceur, 1990):

$ɛ1=ɛ∞-ɛ∞ωp24π2c2λ2ɛ2=ɛ∞ωp2(2πc)τ3λ3$

where τ is the relaxation time, ɛ is the high frequency limit of the dielectric constant and ωp is the plasma frequency given by: $ωp2=4π Ne2ɛ∞me*$

with N being the charge carrier’s density and $me*$ is the effective mass of the charge carrier. The variations of ɛ1(λ) as a function of λ2 and ɛ2(λ) as a function of λ3 are represented in Fig. 6. It is found that, in the infrared range, ɛ1 is a linear function with λ2 while ɛ2 is linear with λ3, allowing thus to determine ɛ, ωp, τ and $Neme*$. Their calculated values are summarized in Table 2. The value of ɛ of about 8 is higher than those of La doped NiO and Li doped ZnO binary ones. However, ωp values remain in 3~9×1014 rd/s domain which matched well with those of the same oxides (Mrabet et al., 2016; Salah et al., 2017).

### Electrical Conductivity Study

The impedance spectroscopy is considered as a powerful technique to investigate the performance of the electrical conduction mechanisms inside a thin film material. In this work, the impedance data plots are used to determine both dc and ac conductivity of Mn3O4:Zr thin films.

Undoped Mn3O4 thin films
The impedance analysis

Nyquist plots (−Z″ vs. Z′) of undoped Mn3O4 thin film extracted from the impedance spectroscopy measurements in the temperature range from 320°C to 450°C with a pitch of 10°C are given in Fig. 7. Generally, the impedance analysis provides the information about the contribution of the relaxation process of different micro regions in the polycrystalline material such as grain, grain boundary and electrode interfaces, the semi-circle behavior of complex impedance plots of each micro region could be thus explained on the basis of an equivalent circuit model consisting of a combination series of grain (high frequency region) and grain boundary elements boundaries (low frequency region) (Larbi et al., 2014; Luo et al., 2016; Xu et al., 2015; Yadav et al., 2016; Yang et al., 2016). So, characteristically, two semi-circular arcs should be observed with non-zero high-frequency intercepts. However, as can be seen in the diagrams, the display of impedance data in the complex plane plot appears in the form of succession of only one depressed semicircle (in each temperature) indicating a non-Debye relaxation of the electrical ac response. This remains with the absence of a second semicircle confirming that the polarization mechanism corresponds to the bulk effect arising in a semi conductive grain. From the features of these semicircles, it can be deduced that the resistance of the thin films decreases with the temperature indicating a semiconducting behavior of hausmannite thin film manifested by the thermal activation of the electrical conduction in both ac and dc regimes. The variations of the imaginary part Z″ of the complex impedance of undoped Mn3O4 as a function of the frequency, for different temperatures, are represented in Fig. 8. As could be seen, for a given temperature, Z″ increases with frequency and a relaxation peak is developed in the spectra, which is shifted to the high frequency side with increasing the temperature showing a decrease in amplitude. This implies that the transient polarization phenomenon is temperature dependent and could be explained as follows: at high temperature, the steady state conduction mechanism is attained rapidly instead of a long time as at low temperatures. However, at high electric fields, whatever the temperature, the steady state is reached almost instantly suggesting that these polarization effects predominate only at low fields. The maximum of Z″ gives the relaxation frequency fMax which is governed by Arrhenius law:

$fMax=f0 exp(-EAkT)$

where EA is the activation energy of the relaxation process and f0 is a characteristic frequency expressed by 2πf0τ=1 where τ corresponds to the characteristic relaxation time of the phonons. From Fig. 9 two temperature ranges could be distinguished; for high temperatures (>420°C) the activation energy is of the order of EA2=0.24eV which is lower compared to that determined for the lowest temperatures (EA1=0.70eV) confirming thus an important dependence of the electrical conduction withthe temperature (Table 3).

Conductivity study

ac conductivity. Fig. 10 reveals the frequency dependent conductivity of undoped Mn3O4 thin film at different temperature ranges. It can be seen that the frequency dependence of conductivity shows two distinct regimes: i) at lower frequencies and at higher temperatures, the conductivity shows a flat response (the presence of plateau) corresponding to the frequency independent conductivity σdc obtained by extrapolating the conductivity value to the lower frequency. This could be attributed to the long range transport of the mobile ions in response to the electric field, where the only successful jumps to its neighborhood vacant site due to the available long time period contributes to the yields dc conductivity σdc as explained previously by Funke using a jump relaxation model (Funke, 1993; Mahajan et al., 2014). ii) In the high frequency region (dispersion region), the conductivity has an ωs dependence and can be explained in terms of polaron hopping, using Jonscher’s power law:

$σ=σdc(1+Aωs)$

where σ is the ac conductivity, σdc is the limit of a zero frequency conductivity, A is a pre-exponential constant, ω=2πf is the angular frequency and “s” is the material intrinsic property dependent constant. From the same figure (Fig. 10),it is observed that the high frequency dispersion region starts to decrease anddisappears by increasing the temperature. Thereby, the characteristic frequencyωp also known as the hopping frequency, at which the relaxation effects begin to appear, moves towards the higher frequency with the increase of the temperature. As shown in Fig. 11, the electrical conduction mechanism is tributary to “s” values. In fact, three different regions could be distinguished:

• A low-temperature region (<350°C), for which the activation is performed at low frequency (~2 KHz) with high and constant exposure (same slope).

• A region of intermediate temperatures (350°C~390°C) in which the conduction is activated at high frequencies (~40 KHz) with a power exponent of the order of “s=1” that decreases with the temperature suggesting that the correlated barrier hopping (CBH) model may be suitable to explain the conduction mechanism in Mn3O4 thin film.

• A region of relatively high temperatures (≥400°C) in which the conduction is activated at high frequencies (~40 KHz) with “s” value lower than 0.5 showing a decrease with the temperature.

Different hopping mechanisms are reported to predict temperature dependent value of “s”. A more detailed explanation will be presented in detail in the following sections.

σdc behavior

The variation of σdc with temperature is shown in Fig. 10. As it could be seen, the dc conductivity increases with the temperature proving that the conduction is thermally activated, and may obey to Arrhenius law:

$σdc=ATexp(-EAkT).$

To reach the activation energy values, Ln(σdcT) curves are plotted in terms of the inverse of the temperature, Fig. 12. Two activating energies were observed. At low temperature, the conductivity shows an activation energy of approximately 0.69 eV, matching well with that found along the frequency study, which implies that the static (long range of nature) and dynamic behaviors are of the same scope. However, at high temperatures, the activation energy is found to be equal to 0.57 eV significantly greater than that of the frequency study, proving that the two relaxation processes are of different scope. Generally, at low frequencies, the dominant polarization process in undoped Mn3O4 thin film may be explained as a local displacement of electrons by hopping mechanism between Mn2+ and Mn3+ ions and an orientation of electric dipole in the direction of the applied field. Also, the enhancement of the σdc could be assigned to the presence of Mn3+ vacancies at octahedral sites leading to the creation of Mn4+ ions at the octahedral sites as reported previously by Bose and Biju (2015a) or else by the increase in drift mobility of charge carriers at higher temperatures as explained by Jain et al. (2016). Thus, according to our results, the gradual decrease in the activation energy with increase in conductivity confirms that the conduction is temperature dependent.

Power exponent “s”

The evolution of the exponent of power “s” as a function of temperature is shown in Fig. 11 indicating the presence of three zones:

• A low temperatures; where the power exponent “s” is a constant and has value slightly greater than 1 indicating a super-linear character of the electrical conductivity. The invariance of “s” in this zone can be explained by the fact that the conduction is done by tunneling (quantum mechanical tunneling, QMT). In this model, “s” value is given by:

$S=1-4Ln(1ωτ0)$

where τ0 is the relaxation time of the jump between two sites, the product ωτ0 is generally much greater than 1. Such a statement does not explain the fact that “s” is greater than 1. To explain this, it is necessary to take into consideration the thermal effect. In such situation, the form of “s” becomes:

$S=1+4WkT-Ln(1ωτ0)$

where W is the barrier height between two sites, a superlinear case is observed for:

$WkT>Ln(1ωτ0)$
• An intermediate temperature zone; where the power exponent is slightly less than 1 and decreases with temperature. Such behavior is in good agreement with the CBH model. According to this model, “s” value can be written as:

$S=1-6kTWM-kTLn(1ωτ0)$

where WM is the difference between the bipolaron level and the conduction band energy.

The variations of $11-s$ as a function of the inverse of the temperature (Fig. 13), allow us to obtain WM value, which is about 1.5±0.2 eV, Table 3.

It is noted that the change of “s” behavior with the temperature is accompanied by a change of Z″ as a function of the frequency (fMax passes from 2 kHz to 40 kHz). This behavior could be linked to the fact that an oxidation in air of Mn3O4 may occur to form Mn2O3 phase for temperatures of electrical measurements situated in 350°C~370°C domain. In fact, for this temperature interval the oxygen/manganese ratio varies in a moderate way (the value of O/Mn ratio increases from 1.33 to 1.50).

Indeed, we consider then the possibility of oxidation of Mn3O4 hausmanite thin film and its transformation into Mn2O3 and this is understood as a decrease of Mn2+ ions within Mn3O4 matrix according to the following reaction scheme:

$2 Mn3O4+1/2 O2→3 Mn2O3.$

It is worth noting that this phase transformation due to oxidation is well-anticipated because, according to previous studies concerning manganese oxide materials, such a change is predictable by means of results conducted by Grundy et al. (2003) and Jacob et al. (2011). In the same line, this oxidation seems to be reinforced by the presence of Zr doping. Indeed, the disappearance of the plateau at T<350°C in the presence of Zr (as ZrOx, ZrO2 secondary phase inside the doped films) increases the oxidation process and hence the absence of the plateau for 12%~20% Zr content domain as mentioned in the following sections. Consequently, in undoped sample, the QMT model corresponds to Mn3O4 thin film while the CBH model is that of the transformed Mn2O3 layer in this latter where the conduction mechanism is provided by the large polaron hopping, Fig. 14. For temperatures exceeding 400°C, the power exponent “s” has low values; this behavior can be explained in two different ways:

• at high temperatures domain, the density of free charges increases and consequently their contribution to conduction becomes preponderant (Conduction by the free charges is independent of the frequency), hence a decrease in the conduction dependence with frequency. Or/

• the conduction process as being is due to diffusion of thermally activated holes trapped at Mn3+ (following the formation of Mn2O3) rather than the chargecarriers production. This assumption leads to the conclusion that the electricalconduction is due to an increase in the mobility of the charge carriers.

The effect of Zr doping in Mn3O4 thin films

### The impedance analysis

The Nyquist diagrams of the different films of x at.% Zr doped Mn3O4 (with x=3, 6, 12, and 20) are represented in Fig. 15. It is found that as doping increases until 12 at.%, the diameter of the semicircle type arc which gives the electrical resistivity of the samples becomes more and more flattened proving that the distribution of relaxation time becomes increasingly wider leading to a decrease in resistivity. This decrease in resistivity which is probably due to an increase in the charge carriers concentration, could be attributed to the substitution of Mn2+ ions by Zr4+ ions as reported elsewhere (Funke, 1993)Such interpretation could be supported by previously reported theoreticalstudies that suggest that the formation energy of ZrZn defect is the lowest compared with that of interstitial Zr (Zri) and substitutional Zr for O (ZrO). This indicates that ZrZn defect forms easier and its concentration may be the highest in doped films (Wang et al., 2008).However, when the doping reaches 20 at.%, the resistance increases againwhich could be explained by the fact that Zr element cannot incorporate into Mn3O4 matrix and it remains as an impurity in various forms of ZrOx or ZrO2, which lead (Herodotou et al., 2015; Lv et al., 2008; Paul et al., 2003; Wang et al., 2014). These results are consistent with those found elsewhere (Said et al., 2017).The curves giving the imaginary parts of the impedance as a function of thefrequency for Zr doped Mn3O4 thin films (with x=3, 6, 12, 20) are also illustrated in Fig. 16. The relaxation frequencies fMax giving the maximum of Z″ increase with the temperature for all the samples following the Arrhenius law. It is also noted that in comparison with undoped Mn3O4,the amplitude of Z″ decreases especially for 3 and 12 at.% Zrdoped Mn3O4 samples, indicating possible accumulation of free charges in the grains further to the ionization of the Zr atoms on Mnsites, where Zr4+ ions replace Mn2+ ions giving two extra electrons to the system. Always in comparison with undoped Mn3O4 thin film, doped ones have the relaxation frequency fMax shifting to higher frequencies showing a noticeably decrease in phonon’s relaxation time. As a matter of fact, the dielectric relaxation time is closely related to the electrical conductivity. Indeed, it is a measure of how long relaxation phenomenon takes to become neutralized by conduction process. This being so, one could conclude that zirconium doping could reinforce the metallic character of these films. On the other hand, the curves related to Ln(fMax) as a function of 1/T for different films are displayed in Fig. 17. The corresponding activating energies are indicated on the curves and gathered. It is noted that, with the exception of 6 at.% Zr doped Mn3O4,the different films possess 2 activating energies: the first is related to lowtemperatures domain and the second is for high temperatures one. These energiesdo not exhibit a constant monotone with the Zr content which may be due to threeplausible reasons:

• possible incorporation of Zr into Mn3O4,

• possible moving of Zr ions from their interstitial sites to form ZrOx entities as secondary phases or/

• Zr might reached solubility limit in Mn3O4 matrix. In fact, at low temperatures, the increased of oxygen induced by ZrMn and Zri are short range motion at relatively low Zr content (except for 6 at.%).

As a result, EA1 gives minimum value in this doping range. However, at the highest doping level (i.e., 20 at.%), the oxygen is pinned by Zr that moved from their interstitial sites to clusters and form secondary phases and became long range motion, reducing thus the diffuseness of Zr. Consequently, EA1 reached a high value of about 0.87 eV which corresponds to the activation energy of conduction caused by oxygen vacancies, that is around 1 eV. Moreover, the increase of the temperature has an intricate influence on EA2 activation energy. In fact, the ionic diffusion via the structural defaults and interstitial atoms in addition to impurities depend strongly on the temperature. In view of these intricacies, we do not have a reliable explication of high temperature influence on the activation energy because the phenomena overlap and we cannot isolate each of them.

### Conductivity study

ac conductivity. The curves displayed in Fig. 18 give the variations of the conductivity in terms of the frequency for different Zr doped Mn3O4 thin films. It is found that in low temperatures (<350°C) for which the activation is carried out at low frequency (~2 kHz), it remains for the doped films having concentrations of 3 and 6 at.% and disappears for Zr 20% doped film. This can be explained by the fact that Zr doping blocks the oxidation of Mn3O4 to form Mn2O3 and thus opposes the insertion of the oxygen into the layer as as it is detailed above (see Power exponent “s” subsection, 140 pages).

σdc behavior

The variations of the conductivity measurements, at low frequencies, as a function of the inverse of the temperature are represented in the Fig. 19. We note that, as for Ln(fMax), with the exception of 6 at.% Zr-doped Mn3O4,the measurements show two energies of activations corresponding to low and hightemperatures. These energies present indeed an absence of monotony feature withZr concentration. The activation energies, whether at low or high temperaturesare close and quite high values compared to those found by the frequency studywhich could be explained by a long range nature of relaxation process.

Power exponent “s”

The variations of the power exponent “s” as a function of the temperature for different Zr doping are shown in Fig. 20.

We notice indeed the following relevant facts:

• The super-linear conduction zone has disappeared for 20 at.% Zr doped film which reinforces the idea that the oxidation of Mn3O4 to Mn2O3 has been blocked by the use of a relatively high Zr content.

• In the intermediate zone (350°C~390°C) especially for the 3, 6, and 12 at.% Zr doped films, the conduction admits always a mechanism according to CBH model with a greater barrier WM (Fig. 21), indicating that the defaults level approximates the valence band one.

CONCLUSIONS

In summary, we have addressed the issues regarding the change of the electric mechanisms within Zr doped Mn3O4 hausmanite thin films through an oxidation in air around the temperature of the order of 350°C. This contribution seems so interesting to illuminate some intrigue phenomena concerning the stability of such binary oxide material with respect to an oxidation caused by the annealing temperature. Such electrical investigations which have so far been thoroughly addressed in this work may be of interest for possible use of these films in several interesting applications which have recently emerged at the forefront of potentials research such as the photocatalysis, gas and bio-sensors and so on.

Figures
 Fig. 1. Configuration of substrate/Mn3O4 thin film/Ag samples for the electrical measurements.
 Fig. 2. Refractive index n (λ) and extinction coefficient k (λ) of undoped and Zr doped Mn3O4 thin films.
 Fig. 3. Refractive index vs. 1/λ2, in the visible range, of undoped and Zr doped Mn3O4 thin films.
 Fig. 4. Plots of as a function of (hυ)2, in the visible range, for different doping level.
 Fig. 5. Dielectric constants ɛ1 (λ) and ɛ2 (λ) of undoped and Zr doped Mn3O4 thin films.
 Fig. 6. ɛ1 vs. λ2 and ɛ2 vs. λ3 of undoped and Zr doped Mn3O4 thin films.
 Fig. 7. Complex impedance spectra as a function of temperature of undoped Mn3O4 thin film.
 Fig. 8. Frequency dependence of Z″ at various temperatures of undoped Mn3O4 thin film.
 Fig. 9. Plot of ln(fMax) versus 1,000/T of undoped Mn3O4 thin film.
 Fig. 10. Plot of ac conductivity as a function of frequency at different temperatures for undoped Mn3O4 sample.
 Fig. 11. Temperature dependence of the angular frequency exponents.
 Fig. 12. Plot of Ln (σdcT) versus 1,000/T.
 Fig. 13. Plot of WM for pure Mn3O4 film.
 Fig. 14. Energetic diagram of defects in Mn3O4 sprayed thin film.
 Fig. 15. Complex impedance spectra as a function of temperature of 3 at.% (A), 6 at.% (B), 12 at.% (C), and 20 at.% (D) Zr doped Mn3O4 films.
 Fig. 16. Frequency dependence of Z″ at various temperatures of Zr doped Mn3O4 thin film deposited at various doping concentration.
 Fig. 17. Plot of Ln(fMax) versus 1,000/T of Zr doped Mn3O4 films at various atomic concentration of Zr.
 Fig. 18. Plot of ac conductivity as a function of frequency at different temperatures for Zr doped Mn3O4 at different temperatures.
 Fig. 19. Ln(T) versus 1,000/T for Zr doped Mn3O4.
 Fig. 20. Temperature dependence of the ‘s’ parameter for different doping level.
 Fig. 21. Plot of WM barrier for all the samples doped with different Zr content Mn3O4.
Tables

Values of A and B constants relative to the Cauchy model for each doping level along with other relevant constants

Zr concentration (at.%) A B (μm2) E0 (eV) Ed (eV)
0 2.579 0.285 14.78 2.60
3 2.049 0.656 5.84 1.71
6 2.033 0.863 5.37 1.55
12 2.297 0.777 7.47 1.67
20 2.25 0.956 5.62 1.48

Values of the dielectric parameters deduced from optical measurements

Zr concentration (at.%) ζ ωp (1014 rad s−1) T (10−14 s) $N/me*(1048 cm-3 g-1)$
0 7.94 3.54 2.62 3.43
3 6.38 4.64 2.14 4.73
6 7.46 5.85 3.24 8.80
12 8.36 7.9 3.34 18.00
20 8.19 5.78 5.02 9.43

Some electrical parameters of the Zr doped Mn3O4.

Zr concentration (at.%) Activation Energy (eV) Wm (eV)

EA(Z) EA(σDC)

EA1(Z) EA2(Z) EA1(σDC) EA2(σDC)
0 0.70±0.02 0.24±0.05 0.69±0.03 0.57±0.01 1.5±0.2
3 0.54±0.03 0.38±0.04 0.63±0.02 0.72±0.05 1.83
6 1.06±0.04 0.9±0.02 2.30
12 0.48±0.03 1.15±0.07 0.72±0.04 0.38±0.03 2.40±0.3
20 0.87±0.04 0.16±0.02 0.78±0.03 0.83±0.14 -

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