J. Nig. Soc. Phys. Sci. 5 (2023) 1180 Journal of the Nigerian Society of Physical Sciences Optical, Dielectric and Optoelectronic Properties of Spray Deposited Cu-doped Fe2O3 Thin Films A. Y. Fasasia, E. Ajenifujaa,∗, E. Osagiea,d, L. O. Animasaunc,d, A. E. Adeoyeb, E. I. Obiajunwaa aCentre for Energy Research & Development, Obafemi Awolowo University, Ile-Ife, Nigeria. b Technical University, Km 15, Lagos Ibadan Expressway, Ibadan, Oyo State, Nigeria. cDepartment of Physics, Electronics & Earth Sciences, Fountain University, Osogbo, Osun State, Nigeria. dPhysics & Engineering Physics Department, Obafemi Awolowo University, Ile-Ife, Nigeria. Abstract Copper-doped hematite thin films were prepared by spray pyrolysis technique using a mixture of ethanol and distilled water precursors. Visual observations showed that aqua precursor produced films of less integrity compared with ethanol that produced thin, uniform and transparent yellowish-brown films that adhered well to the substrate. Composition and thickness measurements determined by RBS revealed that ethanol precursor produced thinner films of 94.45 and 51.77 nm while aqua precursor produced films of 1,370 and 1,120 nm for undoped and Cu-doped Fe2O3 respectively. This is an indication that ethanol solutions produced nano-thick films of high integrity. The composition revealed that only the Cu-doped Fe2O3 deposited by ethanol solution gave composition close to stoichiometric Fe2O3 while the others gave non-stoichiometric Fe (OH)3. Optical characterization carried out using UV-visible spectrophotometer in transmittance mode indicated that the film thickness was directly proportional to the number of passes which is inversely proportional to the transmittance. Three bandgap determination methods namely; Tauc, Absorption Fitting Spectrum (AFS) and Davis-Mott were employed with the result that Tauc and AFS gave close direct and indirect bandgap energies (Eg) of 3.44 and 1.98 for AFS and 3.43 and 2.32 eV for Tauc respectively. The Urbach tail energy determined was 1,100 meV which is an indication of a broad onset of absorption. The steepness parameter (σ) was found to be 7.83 while the electron-phonon (Eph) coupling energy was found to be 0.85 eV. It was also observed that the refractive index (n) was about 15 times greater than the extinction coefficient (k). In the study of the dispersion parameters using single oscillator and Sellmier models, the values of the single oscillator energy (Eosc), dispersion energy (Ed), zero frequency dielectric constant (�o), zero frequency refractive index (no), the average oscillator strength (So), the average oscillator parameter (λo) and the dispersion parameters were determined. All the values of the parameters estimated are of the same order of magnitude with other semiconducting materials. The study showed that Cu-doped Fe2O3 could be employed as dielectric material as well as in optoelectronic devices. DOI:10.46481/jnsps.2023.1180 Keywords: Thin film, bandgap, Urbach energy, refractive index, dispersion parameters, oscillator parameters Article History : Received: 07 November 2022 Received in revised form: 13 March 2023 Accepted for publication: 15 March 2023 Published: 14 June 2023 c© 2023 The Author(s). Published by the Nigerian Society of Physical Sciences under the terms of the Creative Commons Attribution 4.0 International license (https://creativecommons.org/licenses/by/4.0). Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Communicated by: E. A. Emile ∗Corresponding author tel. no: +2348057415551 Email address: eajenifuja@gmail.com ( E. Ajenifuja ) 1. Introduction Metal oxides possess a broad range of electrical, chemical, and physical properties that are often highly sensitive to changes in their chemical environment. Because of these 1 Fasasi et al. / J. Nig. Soc. Phys. Sci. 5 (2023) 1180 2 properties, metal oxides have been widely studied and specific applications are based on appropriately structured and doped oxides [1]. The enhancement in the gas sensing performance of metal oxides by electron, ultraviolet, and plasma irradiations was due to the modified surface structure [2]. Nanocrystalline transition metal oxide particles and films have found consider- able interest in recent years because of their special properties, such as a large surface-to-volume ratio, increased activity, special electronic and unique optical properties, as compared to those of the bulk materials. The oxides of transition metals are an important class of semiconductors, which have applica- tions in magnetic storage media, solar energy transformation, electronics, and catalysis [3]. Magnetic nanoparticles of iron oxide due to their biocompatibility, catalytic activity, and low toxicity have dragged significant attention for their applications in various fields of medical care such as drug delivery systems, cancer therapy, and magnetic resonance imaging. Apart from the biomedical applications, these iron oxide nanoparticles are of technological importance due to their application in many fields including high density magnetic storage devices, ferro-fluids, magnetic refrigeration systems, catalysis, and chemical/ biological sensors [4]. Fe and O form a number of phases, e.g., FeO (wustite), Fe3O4 (magnetite), α-Fe2O3 (hematite), and γ-Fe2O3 (maghemite). The latter phase is synthetic while the remain- ing oxides occur in nature. The Fe-O phase diagram shows the predominance of the Fe2O3 stoichiometry for most temperature and pressure preparation conditions [5, 6]. Of all the transition metal oxides, α-Fe2O3 has been extensively studied due to its low cost, high chemical stability, nontoxicity, abundance in na- ture, and biocompatibility [7]. Hematite crystals are believed to nucleate and grow from iron (III) organic complex which through hydrolytic breakdown yield nano-sized ferrihydrite ag- gregates that eventually transform to aFe2O3 through dehydra- tion and rearrangement according to the following equation [8]: Fe3+ yield s −−−−→ Fe5O8 · 4H2O yield s −−−−→ αFe2O3 (1) Certain studies believed that without slight deviation from stoichiometry, iron oxide (α-Fe2O3) is a thermodynamically stable oxide of the hexagonal packed crystal structure is con- sidered an insulator with localised Fe3+ ions while with a slight deviation from stoichiometry hematite is an n-type indirect semiconductor with bandgap energy commonly considered to be 2.2 eV [9]. Some studies have also shown that hematite can exhibit both indirect and direct transitions with indirect and direct bandgap energies around 1.9 and 2.7 eV [4, 7, 10–15]. This range of band gap energy has conferred on hematite the ability to be employed in many electrochemical applications since about 29 % of visible light has energies greater than the hematite band gap (2.2 eV) [16] as a result of which α-Fe2O3is capable of absorbing a large portion of the visible solar spectrum (absorbance edge ˜600 nm). With all of these advantages, the usage of α-Fe2O3 has been restricted by many anomalies such as higher electron-hole recombination rate leading to poor electrical conductivity with a hole length of 2 – 4 nm, poor mobility, insufficient ionic diffusion rate leading to low specific capacitance and VB positioning (VB is positive with respect to H+/H2 potential) [9, 17–19]. Several methods have been used to improve on the limi- tations of α-Fe2O3 for improved solar conversion. Enormous efforts were devoted to the modification of the electronic structure of hematite via doping [20], thin film deposition, core-shell structure, and coating. To this end, Sn [21, 22], Ti [20, 29], Si [23, 30], Zn [24], MgO and CaO [26], Ir [27], Zr [31], Cu [32], Ti+Al [25], Ti+Sn [28] –doped and undoped [33, 34] have been employed to dope Fe2O3 individually or in combination as photoanodes for water splitting application. On the other hand, Cr [35, 36], Nd [37], ZnO [38], and Eu [39] have been used to dope α-Fe2O3 for improving the magnetic properties. In the area of portable, flexible and wearable electronics and asymmetric supercapacitors undoped α-Fe2O3 [40, 41], Carbon incorporated α-Fe2O3on carbon nanotube [18], α- Fe2O3/graphene/Ink [42], α-Fe2O3 on carbon cloth [43], oxy- gen vacancy engineered α-Fe2O3 nanoarrays on carbon cloth [44], α-Fe2O3nanorods in Ni/Fe battery [45], MXene@ α- Fe2O3 coreshell /carbon cloth [46], Si@ α-Fe2O3/carbon cloth [47], Polypyrole doped a-Fe2O3 [48], α-Fe2O3@PANI core- shell [49], TiO2@ α-Fe2O3coreshell on array of carbon cloth [50] and Cu-doped α-Fe2O3 [51] have all been employed to in- crease the conductivity of α-Fe2O3For environmental remedia- tion through waste water treatment, α-Fe2O3/Ppy for photocat- alyst degradation of methylene blue under UV irradiation [52], α-Fe2O3in the treatment of oily waste water [53], pure copper and GO-doped α-Fe2O3 [54] for waste water treatment, Cu- doped Fe @Fe2O3 coreshell nanoparticles for removing AS(III) for Smelting waste water [55], Zn-doped α-Fe2O3for photocat- alytic degradation of Rose Bangal dye [56], activated carbon coated α-Fe2O3 adsorbent for chlorinated gas treatment [57], Ni-doped α-Fe2O3for removing toxic metals for aqueous so- lution [58], Y2O3/ α-Fe2O3/TiO2 [59] and α-Fe2O3@CeO2- ZrO2/Polygorskite [60] composite catalysts for treatment of or- ganic pollutants have all been used successfully. As gas sensors, Pd-doped α-Fe2O3 [61], Nb-doped α-Fe2O3 [62], Cu-doped α- Fe2O3 [63], and Ti- α-Fe2O3 [64] have all been synthesised and employed for LPG, NO, NOx, ethanol and CO gas sensing, re- spectively. Different method of synthesis have been used to produce dope α-Fe2O3such as ultrasonic spray pyrolysis [4], DC mag- netron and DC pulsed hollow cathode sputtering system [7], SILAR (10), normal spray pyrolysis [16], flame annealing [21], atmospheric pressure CVD [23], Electrodeposition [31], Co- precipitation [36, 64, 69], combustion synthesis method [37], gelation and polymerisation [52], sol-gel [54, 56, 70], high en- ergy ball milling [58], pulsed laser deposition [65], Filtered arc deposition [67], oxygen- plasma assisted MBE [69]. Of all the methods of preparation, spray pyrolysis offers the ease of preparing small as well as large area coating of thin films and nanopowders at low cost for different technological appli- cations. Moreover, it does not require high quality targets nor 2 Fasasi et al. / J. Nig. Soc. Phys. Sci. 5 (2023) 1180 3 vacuum at any stage of preparation. The deposition rate and the film thickness can be controlled effectively by changing the spray parameters such as the precursor composition, nozzle to substrate distance, flow rate, and the number of passes. Most of the studies on Cu-doped α-Fe2O3 focussed mainly on the application and not on the detailed optical and dielectric stud- ies needed to determine the areas of applications. This study therefore presents detailed optical and dielectric studies of Cu- doped α-Fe2O3 films deposited using spray pyrolysis technique, UV-visible spectrometry and Rutherford backscattering spec- troscopy (RBS). 2. Experimental Procedure The starting solutions were prepared from Iron (III) chlo- ride (FeCl3) and copper (II) chloride (CuCl2) purchased from Sigma Aldrich with ethanol and distilled water as solvents. The salts were analytical grade and used as purchased without further purification. For the aqueous solution, 0.1 M solution of iron (III) chloride was prepared by dissolving 4.0 g of FeCl3 and 2.56 g of CuCl2 in 250 ml of distilled water. For ethanol solution, the same mass of FeCl3 was dissolved in 250 ml of ethanol while CuCl2 was dissolved in a mixture of ethanol: distilled water in the ratio of 200:50 giving four different solutions. The solutions were thoroughly stirred using a magnetic stirrer. The Pyrex glass substrates were cleaned in dilute hydrochloric acid, alcohol, and distilled water and dried in an oven before deposition at a substrate temperature of 320 ± 5 0C and nozzle–to–substrate distance of 23 cm. Suction–based airbrush and air blast atomization was employed for the depositions. For Cu-doped Fe2O3 deposition, the FeCl3:CuCl2 volume ratio of 80:20 was adopted. After deposition, the samples were annealed in a tubular furnace at different temperatures ranging from 350 -500 oC in air. The RBS experiment was performed using the 1.7 MeV Pel- letron Tandem Accelerator at the Centre for Energy Research & Development, Obafemi Awolowo University, Ile-Ife, Nige- ria. For this purpose, 4He2+ ion beam was used as projectile ions. The scattering angle was 165o and the resolution of the detector was 12 keV. During the process of acquiring the spec- tra data, the energy of the ion beam used was 2.2 MeV. All measurements were performed at room temperature with cur- rent varying between 20 and 60 nA at a constant charge of 20 µC. All the spectra were fitted using Windows SIMNRA soft- ware for the determination of the composition and the thick- ness of the films. The optical properties were studied using a Stellanet UV-visible spectrophotometer (Model EP2000) with wavelength covering 200 to 1100 nm in the transmission mode. 3. Results and Discussion 3.1. Visual Observation Typical surfaces of the deposited films are shown in Figure 1 for doped and undoped films. The surfaces are clean and regular without voids with strong adherence to the substrate. The change in colour due to Cu addition is obvious. Figure 1: Surfaces of the undoped (left) and Cu-doped (right) Fe2O3 deposited films taken by an optical camera Camon 12 Pro. 3.2. RBS Study - Determination of the Thickness and Compo- sition. Preliminary results of the RBS analyses of the four films grown on Pyrex glass using ethanol and distilled water as sol- vents for doped and un-doped Fe2O3 is presented in Figure 2 (a-d). The shape of the spectra clearly showed the effect of the solvent employed in depositing the films. Sharp peaks are associated with ethanol while broad peaks are associated with distilled water. This may be due to the film thickness and the de- gree of structural orderliness. All the films deposited using dis- tilled water for the same number of passes are 15 times thicker than the films deposited using ethanol as shown in Table 1. This may also be an indication of the film integrity in that alcohol so- lutions produced more ordered films than distilled water. The spraying process employed in this study can lead to the formation of films of FeOH, FeO, Fe2O3, or Fe3O4. In a pure crystal the ratio of atomic content Fe:O is 0.5:0.5 for FeO, 0.4:0.6 for Fe2O3, 0.429:0.571 for Fe3O4 and Fe: OH of 0.25:0.75 for Fe(OH)3. From the elemental composition of the films, we can deduce that the films are neither FeO nor Fe3O4. The RBS simulation of the films gave the atomic percentage of Fe, O and Cu. The results, using Fe/O values in Table 1, indicate that undoped alcohol and undoped distilled water precursors produce non-stoichiometric films of Fe(OH)3 with anion deficiency compensated by excess cation for undoped alcohol precursor and cation vacancies compensated by excess oxygen for undoped aqua precursor. In the case of Cu-doped precursors, distilled water also produce non-stoichiometric films of Fe(OH)3 but with Ca substituting for Fe and both anion and cation vacancies are probably compensated by Cu. This explains the high content of Cu in the film but does not explain the incursion of Ca into the film. To explain the presence of Ca in the film, the RBS of the substrates for each film were also analysed simultaneously with the film and the result is shown in Table 2. It is obvious from the table that Ca did not diffuse from the substrate into the film and therefore we may infer that Ca got introduced into the film from the distilled water used as a solvent. But there is no presence of Ca in the undoped aqua precursor and this led us to believe that Cu must have acted as a catalyst in the film formation and coexisted in the film without forming a compound with Fe. Lastly, for Cu-doped ethanol precursor producing film thickness of 51.77 nm, the Fe/O ratio of the film gave a value of 0.660 which is very close to 0.667 for pure Fe2O3. It can then 3 Fasasi et al. / J. Nig. Soc. Phys. Sci. 5 (2023) 1180 4 Figure 2: RBS spectral of undoped and Cu-doped Fe2O3 in ethanol (a, b) and undoped and Cu-doped Fe2O3 in distilled water (c, d). be said that Cu acted as a catalyst for the formation of Fe2O3 and existed in the film as a solid solution without forming a def- inite phase in the film. Hence, from this point, further analyses will focus solely on Cu-doped alcohol precursors. 3.3. Transmission Analyses The effect of the number of passes on Cu-doped Fe2O3 is depicted in Figure 3a where it can be seen that the increase in the number of passes led to a decrease in transmittance. This trend had been observed in CuO film deposited by spray pyrol- ysis [71]. Two distinct regions can be observed on the spec- tra with the line of demarcation around 648 nm which corre- sponds to 1.92 eV. At this wavelength, the transmittance for 40, 60, and 80 passes were 85, 82, and 78% respectively. Above this wavelength is region 2 where the transmittance is slowly varying as the wavelength increases. Below this wavelength is region 1 where the transmittance is rapidly changing as the wavelength decreases. Region 1 is the absorbing region with 80 passes having the highest absorbance which is probably due to the increased thickness of the film as the number of passes increased while region 2 is the transparent region. This result showed that the film is slightly opaque to photon energies less than 1.92eV and that it can serve as an optical window and a good solar absorber material. Figure 3b is the comparison of the transmittance of Cu-doped Fe2O3 films grown on borosil- icate glass with 80 passes using deionized water and alcohol. The graph shows that deionised water produced thicker film due to the low transmittance (maximum of 30%) while ethanol pro- duced thinner films of high transmittance (maximum of 80 %). This corroborates the results obtained from RBS. 3.4. Absorption Coefficient and Skin Depth 3.4.1. Absorption Coefficient The absorption coefficient α of a semiconducting material is an important parameter useful in determining how the incoming photon energy interacts with the atoms of the semiconductor. The absorption coefficient was calculated using the relation α = 1 t ln ( 1 T ) (2) Since it is a function of the energy of the incoming pho- ton, Figure 4a depicts the variation of the absorption coefficient with the wavelength of the interacting photon where it can be seen that the absorption is high at high photon energy (ultravio- let region) and decrease gradually till 700 nm where it becomes invariant at the lowest value of 5.0 × 104 cm-1. This trend has been observed in many films even prepared with different meth- ods [72]. The high value of the absorption coefficient makes the material a good absorber and very useful in optoelectronic ap- plications. 4 Fasasi et al. / J. Nig. Soc. Phys. Sci. 5 (2023) 1180 5 Table 1: Thickness (nm) and composition (at. %) of the annealed films from RBS analyses. Precursor Thickness Fe O Cu Ca Fe:O Fe/O Remark Undoped alcohol Soln 94.45 nm 27.83 72.17 ----- ----- 0.278 : 0.723 0.359 Fe(OH)3 Cu-doped alcohol Soln 51.77 nm 39.35 59.62 1.03 ----- 0.394 : 0.596 0.660 Fe2O3 Undoped aqua Soln 1370 nm 17.85 82.15 ----- ----- 0.179 : 0.822 0.217 Fe(OH)3 Cu-doped aqua Soln 1120.80 13.56 69.26 4.40 12.77 0.136 : 0.693 0.196 Fe(OH)3 Table 2: Composition (at. %) of the substrate employed for the films Film Thickness (nm) Ca Si O Fe Na Al Fe2O3/ alcohol 94.45 1.83 28 56 0.52 12.6 0.53 Cu-Fe2O3/ alcohol 51.77 1.83 28 56 0.52 12.6 0.53 Fe2O3/ distilled H2O 1370 1.83 28 56 0.52 12.6 0.53 Cu-Fe2O3/ distilled H2O 1120.80 1.83 28 56 0.52 12.6 0.53 3.4.2. Skin Depth On the other hand, when a ray of light passes through thin films, the photon intensity decreases dramatically for many rea- sons, like the density of the material, refractive index, morphol- ogy of the surface, and the film microstructure. The thickness of the film that causes the intensity of the photon to be re- duced to 1/e value below the surface of the film is called the skin depth δ which is defined as the inverse of the absorption coefficient δ = 1 α . It is therefore a function of frequency and hence the band gap. Fig. 4b is depicting the connection be- tween the skin depth and photon energy of Cu-doped Fe2O3. The gradual decrease in skin depth can be seen until it gets to a minimum depth of 2.68 x 10-6 cm (26.8 nm) at around 4 eV (λ = 342 nm). This minimum skin depth of 26.8 nm cor- responds to the middle of the film. This result is contrary to other studies where it was shown that the skin depth reduced to zero at a certain energy corresponding to the cut-off wave- length λcutoff [72, 73]. This may be because the nature of their films was glassy and contain a mixture of crystalline and amor- phous phases whereas the film in this study may be completely crystalline. 3.4.3. Bandgap determination For the photon energy range corresponding to the transmit- tance spectra, the absorption coefficient can be approximated by simple expressions. For example, assuming a parabolic E versus k relationship, the absorption in semiconductors and di- electrics films can be expressed as α = B ( hν− Eg )m hν for hν > Eg (3) The quantity α is the absorption coefficient, hν denotes photon energy, B is a constant that includes information of the convolution of the valence and conduction band states and on Figure 3: (a) Effect of the number of passes on the transmittance of Cu-doped Fe2O3 and (b) comparison of the effect of precursor solvent on the transmit- tance for 80 passes. the matrix elements of optical transitions which is assumed to be independent of energy, EG is the Tauc’s optical gap and B depends on the material composition and deposition method and conditions, m is the order of transition that take values of 1/2, 2, 3/2 and 3 representing direct allowed, indirect allowed, direct forbidden and indirect forbidden transitions, respectively. Other approximations such as the Absorption Fitting Spec- trum (AFS) procedure and David-Mott model exist for deter- mining the band gap of semiconducting materials. Absorp- tion Fitting Spectrum [74] uses equation (3) but is expressed 5 Fasasi et al. / J. Nig. Soc. Phys. Sci. 5 (2023) 1180 6 Figure 4: Graphical representation of the variation of (a) the absorption coeffi- cient with wavelength and (b) the skin depth with photon energy for Cu-doped Fe2O3 from ethanol solution. in terms of “λ”. Rearranging equation (3) gives αhc λ = B ( hc λ − hc λg )m (4) where for direct transition (m = 1/2) and indirect transition (m = 2), we obtain( α λ )2 = K ( 1 λ − 1 λg ) and ( α λ ) 1 2 = C ( 1 λ − 1 λg ) (5) where λg, h, and c are the wavelength corresponding to the optical bandgap value, Planck’s constant, and the velocity of light respectively. Davis and Mott on the other hand proved that through the in-depth analysis of the matrix elements for transitions between extended states and those between weakly localized states, the absorption coefficient (α) can be expressed through the following equation [75–77] αhν = 4πσmin 3πc (∆E)2 (hν− E2) 3 . (6) This can be re-written as: (αhν) 1 3 = K (hν− E2) , (7) where σmin = ( 2π3 c2 h3 a m2 ) [N (Ec)] 2 is the minimum metallic conductivity and E2 = Ec − Ev. Thus plotting (αhν) m against hν for Tauc approximation, ( α λ )m against 1 λ for AFS procedure and (αhν)m against hν for Davis-Mott model where m = 1/2 or 2 for direct and indirect electronic transitions in the case of Tauc and AFS but m = 1/3 or 2/3 for direct and indirect transitions in the case of Davis-Mott, which actually represent direct forbidden and indirect forbidden transitions respectively, we obtain Figure 3. Graphical representation of equations (3), (5) and (7) for determining the bandgap is depicted in Figure 3 (a-c) and the result is presented in Table 3. It can be observed that for direct electronic transition, the three models gave almost equal values of 3.11, 3.44, and 3.43 eV while for indirect electronic transi- tion the disparity in the values is wide, 3.44, 1.98, and 2.32 eV. Since it is a known fact that the direct band gap energy is always higher than an indirect band gap energy, the Davis-Mott model does not reflect this trend and therefore can be neglected. On the other hand, AFS and Tauc models follow this trend and can lead us to say that Cu-doped Fe2O3 has an indirect bandgap that lies between 1.98 and 2.32 eV and a direct band gap of 3.43 eV. This can be explained by noting that the initial orbital assignments of the bandgap suggested it was due to an indirect transition of Fe3+ d–d origin and that a stronger direct transition involving a charge transfer from an O2p orbital to Fe3d did not occur until 3.2 eV [11]. The result indicates that Fe2O3 pre- pared through ethanol solution is an indirect band gap material though many researchers concluded that Cu-doped Fe2O3 can exhibit both a direct and an indirect bandgap transition [10–15]. Table 3: Analyses of the different models employed in determining the band gap of Cu-doped Fe2O3 film. Model Direct (eV) Indirect (eV) Davis-Mott 3.11 3.44 AFS 3.44 1.98 Tauc 3.43 2.32 3.4.4. Urbach band tail energy At photon energies below the exponential absorption edge, there is a sub-gap absorption that originates from transitions between deep localized electron states in the pseudo-gap and extended states in the conduction and the valence bands. The exponential rise is called the Urbach tail and it appears in poly- crystalline, partially crystalline, and non-crystalline materials, because of the existence of these localized states [78–80]. The relationship between the absorption coefficient and Urbach tail energy is given as α = αoe hν EU , (8) where αo is a constant and EU refers to the energy of the band- tail width (Urbach energy). This energy, EU depends slightly on temperature and is often interpreted as the band-tail width owing to the localized states in the forbidden band gap and as- sociated with the perturbation of the non-crystalline and low crystalline materials [81]. Linearisation of equation (8) and 6 Fasasi et al. / J. Nig. Soc. Phys. Sci. 5 (2023) 1180 7 (a) Band gap determination using AFS model for direct (left) and indirect (right) transition. (b) Band gap determination using Davis-Mott model for direct (left) and indirect (right) transition. (c) Band gap determination using Tauc’s method for direct (left) and indirect (right) transition. Figure 5: Band gap determination plotting ln α against hν gives a straight line where the inverse of the slope is the value of Urbach energy. ln α = ln αo + hν EU (9) 7 Fasasi et al. / J. Nig. Soc. Phys. Sci. 5 (2023) 1180 8 Figure 6: Plot of ln α against hν for Urbach energy determination The plot of ln α against hν is presented in Figure 6 where the straight line nature is observed. The value calculated for Urbach energy from the slope is 1,100 meV. The Urbach energy quantifies the steepness of the onset of absorption near the band edge, and hence the broadness of the density of states. Since a sharper onset of absorption represents a lower Urbach energy, Cu-doped Fe2O3 has a broad onset of absorption. 3.4.5. Steepness Parameter There is another expression that relates the absorption co- efficient α to the band gap energy Eg according to Urbach’s assumption [67–69] given by α = β exp [ σ(hν− Eo) kBT ] , (10) where β is a pre-exponential factor, KB is the Boltzman’s con- stant, T is the temperature, σ is another optical constant called the steepness parameter, Eo is the energy of the transition which depends on the type of transition. If it is a direct transition, Eo = Eg while for indirect transition Eo = Eg ± E ph where E ph is the energy due to lattice vibration. Since we have agreed that this is a direct transition then we can replace Eo with Eg in equation (10). Simplifying the equation by taking the natural logarithm of both sides gives ln α = ln β + σhν KBT − σEg KBT ln α = ( ln β− σEg KBT ) + σhν KBT (11) We then obtain Inαo = [ Inβ− σEg KBT ] and hν EU = σhν KBT (12) ⇒ σ = KBT EU (13) where KB = 8.6173 × 10−5 eV.K−1 and T = 300 K (room temperature). Therefore, we can calculate the steepness pa- rameter σ for Cu-doped Fe2O3 to be 7.83 and the electron- phonon coupling energy, Eph = 2 3σ to be 0.85 eV while αo = 1.03 × 104 cm−1. 4. Refractive index, reflectance and extinction coefficient The refractive index which governs the speed of wave prop- agation, reflectance which indicates the percentage of the wave reflected and the extinction coefficient which shows the propa- gation loss in a material are important parameters in determin- ing the optical properties of thin films to be employed in op- toelectronic devices. In the present study, the reflectance had been determined using the relation: R = 1 + [ T e2.303αt ] 1 2 , (14) where T is the transmittance, α is the absorption coefficient, and t is the film thickness obtained from the RBS study. The refrac- tive index n, the extinction coefficient k and the optical conduc- tivity σ were determined through equations (15) and (16). n = 1 + √ R 1 − √ R (15) k = αλ 4π (16) Figure 7: Plot of n and k against wavelength for Cu-doped Fe2O3 Graphical representation of equations (15) and (16) against wavelength is shown in Figure 7 to understand their variations as photon energy changes. The refractive index showed a high value at high energy and decreased as the wavelength increased and became constant from 700 nm. The extinction coefficient also showed the same trend as the refractive index. Both “n” and “k” became constant from 700 nm up to 1000 nm. The figure also indicated that the refractive index is 16 times higher than the extinction coefficient. The dependence of the index of refraction on photon energy can be well described using 8 Fasasi et al. / J. Nig. Soc. Phys. Sci. 5 (2023) 1180 9 a single-effective-oscillator formulation according to Wemple and Di-Domenico [82, 83] n2 − 1 = Ed Eosc[ E2osc − (hν) 2 ] (17) By taking the inverse of equation (17), we obtain 1( n2 − 1 ) = Eosc Ed − (hν)2 Ed Eosc , (18) where Eosc is the single-oscillator energy and Ed is the disper- sion energy. By plotting ( n2 − 1 )−1 against (hν)2 we obtain a straight line whose intercept equals EoscEd and the slope is 1 Ed Eosc . The graph is presented in Figure 8 where the values of 4.44 and 6.12 eV were obtained for Ed and Eosc respectively. The expression (17) holds for photon energies well below Eosc. At energies approaching Eosc, deviations to the simple law originating from the proximity of the main band-to-band transitions, are measured. Furthermore, the knowledge of Ed and Eosc can be utilized in determining the zero-frequency dielectric constant εo and zero frequency refractive index no through the relation (19), and the values obtained are recorded in Table 4. εo = n 2 o = 1 + Ed Eosc (19) Figure 8: Plot for the determination of the single oscillator energy (Eosc) and the dispersion energy (Ed) Another way of discussing the dispersion parameters is to employ the long wavelength approximation of the single-term Sellmier relation since it retains the physical significance of the oscillator parameters. The relation is given by equation (19), n2 − 1 = S oλ2o[ 1 − ( λo λ )2], (20) where So is the average oscillator strength and λo is the average oscillator parameter. Again, linearising equation (20) gives,( n2 − 1 )−1 = 1 S oλ2o − 1 λ2S o . (21) Figure 9: Graph for determining the average oscillator strength (So) and average oscillator parameter ( λo). Plotting ( n2 − 1 )−1 against λ−2 will give a straight line whose intercept ( 1 S oλ2o ) and the slope is ( 1 S o ) can be determined and the graph is presented in Figure 9. The dispersion param- eter EoS o where Eo = ~c eλo can also be determined. The values of S o, λo and Eo S o determined through this process is tabulated in Table 4. 4.1. Density of State Effective Mass Ratio The relationship between the refractive index “n” and the wavelength of the incident photon can also be employed to de- termine the density of state effective mass ratio and the high frequency dielectric constant through equation (22): n2 = ε∞ − 1 4π2εo ( e2 c2 ) ( Nc m∗ ) λ2 (22) where ε∞ is the high frequency dielectric constant, “e” is the electronic charge, “c” is the speed of light and “Nc/m*” is the density of state effective mass ratio. Plotting n2 against λ2 will give a curve where the intercept of the straight part of the curve on the y-axis equals ε∞ and ( Nc m∗ ) can be determined from the slope which is 14π2εo ( e2 c2 ) ( Nc m∗ ) . With m* = 0.44 mo, the value of Nc can also be calculated. These values of ε∞, Nc/m* and Nc are recorded in Table 4. 4.2. Dielectric constant The knowledge of “n” and “k” permits the determination of the real, imaginary, and loss tangent of Cu-doped Fe2O3 films through equations (23)-(25), and the graphical representation is depicted in Figure 11. εr = n 2 − k2 (23) εi = 2nk (24) tan δ = εi εr (25) 9 Fasasi et al. / J. Nig. Soc. Phys. Sci. 5 (2023) 1180 10 Figure 10: Variation of n2 vs λ2 for the determination of the high frequency dielectric constant ε∞ and the density of state Nc Figure 11: Variation of εr , εi and tan δ with photon wavelength Figure 11 shows that εr is far greater than εi since εi is a product of n and k and with smaller values of k, εi will be lower than εr . It can also be observed that εr , εi and tan δ decreased gradually until around 700 nm where they become independent of the photon wavelength. The variation of these three param- eters is an indication of photon energy interaction with the free electrons of the Cu-Fe2O3 matrix. The low loss tangent (tan δ) means that energy dissipation and propagation loss of the pho- tons in the matrix are low indicating that photons are able to pass freely in the matrix which will lead to increased optical mobility and conductivity. 4.3. Relaxation time, mobility, resistivity and conductivity The variation of the imaginary part of the dielectric con- stant εi with wavelength can also be employed to determine the relaxation time τ, optical mobility “µopt”, optical resistiv- ity “ρopt” and optical conductivity “σopt” through the following equations: εi = 1 4π3εo ( e2 c3 ) ( Nc m∗ ) . 1 τ λ3 (26) Table 4: Elemental composition, optical, dielectric and oscillator parameters for Cu-doped Fe2O3 Parameter Symbol & Unit Cu doped Fe2O3 Iron content Fe (at. %) 39.35 Oxygen content O2 (at. %) 59.62 Copper content (at. %) Cu (at. %) 1.03 Plasma frequency wp (s-1) 6.85 × 1013 High frequency dielectric constant ε∞ 1.81 Film thickness t (nm) 51.77 Density of state effective mass ratio Nc/m* (m-3.kg-1) 5.1 x 1054 Optical carrier charge density Nc (m-3) 2.0 ×1024 Urbach energy Eu (meV) 1,100 Relaxation time τ (s) 1.3 ×10-14 Optical mobility µ (m2.V-1.s-1) 5.2 ×10-3 Optical resistivity ρ (Ω.m) 6.0 x 10-4 Optical conductivity σ (Ω-1m-1) 1.67 ×103 Effective single oscillator energy Eosc (eV) 6.12 Dispersion energy Ed (eV) 4.44 Effective single oscillator energy band gap ratio Eosc/Eg 2.64 - 3.09 Zero frequency refractive index no 1.31 Zero frequency dielectric constant εo 1.72 Average oscillator strength Sosc (m-2) 1.93 ×1013 Average oscillator wavelength λosc (m) 1.95 x 10-7 Average oscillator energy Eo (eV) 6.33 x 1018 Dispersion parameter Eo/So (eV.m2) 3.30 ×105 Bandgap Eg (eV) 1.98 – 2.32 Linear susceptibility χ(1) 5.8 x 10-2 Nonlinear susceptibility χ(3) (esu) 1.79 x 10-15 Nonlinear refractive index n2 (esu) 5.1 x 10-14 µopt = eτ m∗ (27) ρopt = 1 eµopt Nc (28) σopt = 1 ρopt (29) where “e”, “c” and “m*” are the electronic charge, velocity of light and effective mass (0.44 mo) of free charge carriers re- spectively. The plot of εi against λ3 will produce a curve where the slope of the linear part of the curve equals 14π3εo ( e2 c3 ) ( Nc m∗ ) . 1 τ which gave τ to be equal to 1.3 × 10−14s. With this value of τ, 10 Fasasi et al. / J. Nig. Soc. Phys. Sci. 5 (2023) 1180 11 µopt, ρopt and σopt are determined as tabulated in Table 4. The values obtained from this study are of the same order of mag- nitude with the values obtained for some chalcogenide com- pounds [84]. Figure 12: Plot of εr versus λ3 for the determination of the relaxation time. 4.4. Plasma Frequency The relationship between n2 and λ2 given in equation (22) can also be expressed in another form: n2 = ε∞ −  w2p4πc2  λ2. (30) Comparing equation (23) with (30), it can be seen that both equations have the same slope and with the slope of equation (22) determined to be 4.16×109 and equating this value to ( w2p 4πc2 ) which is the slope of equation (30), the value of wρ has been calculated to be 6.85 × 1013 s-1. This value corresponds well with the values obtained by other authors [84]. 4.5. Optical nonlinearity Nonlinear optic happens in a media where the polarization density P responds non-linearly to the electric field E of the light. The non-linearity is typically observed only at very high light intensities. Nonlinear optical phenomena, in which the optical fields are not too large, can be described by a Taylor series expansion of the dielectric polarization density (electric dipole moment per unit volume) P(t) at time t in terms of the electric field E(t): P(t) = εo ( χ(1) E(t) + χ(2) E2(t) + χ(3) E3(t) + · · · ) (31) where the coefficients χ(n) are the n-th-order susceptibilities of the medium, and the presence of such a term is generally re- ferred to as an n-th-order nonlinearity. Simple semiempirical relation based on generalized Miller’s rule allows an estimation of nonlinear susceptibility (χ(3)) and non-linear refractive in- dex (n2) from linear refractive index and/or from the dispersion energy and the energy of effective oscillator of the Wemple-Di Domenico model [84, 85]. The relevant equations are expressed below: χ(1) = Ed 4πEso (32) χ(3) = C  ( n2o − 1 4π )4 (33) n2 = 12πχ(3) no (34) where χ(1), χ(3), no and C are the linear susceptibility, nonlinear susceptibility, nonlinear refractive index and a constant which is equal for all materials with a value of 1.7×10−10 esu and it is independent of frequency. The values obtained using equations (32)-(34) are tabulated in Table 4. 5. Conclusion Cu-doped hematite thin films were prepared from a mix- ture of distilled water and ethanol precursor using spray py- rolysis technique. Apart from RBS studies that provided the film thickness and the composition, all other parameters of the films were deduced from the optical transmittance studies. RBS showed that only the Cu-doped film prepared from ethanol so- lution gave the composition very close to Fe2O3 with film thick- ness of 51.77nm. Optical transmittance studies of the Cu-doped films also showed that the transmittance of the film prepared us- ing distilled water is lower than that of ethanol solution which is an indication that ethanol solution produced nano-thick films of high integrity. Cu-doped Fe2O3 film is highly absorbing with α greater than 105 cm-1. Tauc, AFS and Davis and Mott mod- els were employed to determine the actual value of the bandgap using direct and indirect transition to conclude that Cu-doped Fe2O3 is an indirect bandgap material with 1.98 eV < Eg < 2.32 eV and a direct band gap energy of 3.43 eV. The value of Urbach energy gave an indication of a broad onset of absorp- tion. The variations of the refractive index with photon energy or wavelength allowed the estimation of the single-oscillator energy, dispersion energy, average oscillator strength, average oscillator parameter, dispersion parameter, density of state ef- fective mass ratio, high frequency dielectric constant and the plasma frequency. ε∞ > n2o means that free charge carriers contribute in the polarization process within Cu-doped Fe2O3 thin film. The variation of the imaginary part of the dielec- tric constant (εi) with photon wavelength led to the estimation of the relaxation time, optical mobility, resistivity and optical conductivity. The 1st and 3rd order nonlinear susceptibility and nonlinear refractive index were estimated. All the values of the parameters estimated were of the same other of magnitude with other semiconducting materials. The values also indicated that Cu-doped Fe2O3 film could be suitable for nonlinear, electro- chemical as well as optoelectronic applications. 11 Fasasi et al. / J. Nig. Soc. Phys. Sci. 5 (2023) 1180 12 References [1] Y. Zhu, H. Lu, Y. Lu & X. Pan, “Characterization of SnO2 Films De- posited by D.C. Gas Discharge Activating Reaction Evaporation onto Amorphous and Crystalline-substrates”, Thin Solid Films 224 (1993) 82. [2] C. C. Chai, J. Peng & B. P. Yan, “Preparation and Gas-Sensing Properties of α-Fe2O3 thin Films”, Journal of Electronic Materials 24 (1995) 799. [3] M. Chen, G. Diao & X. Zhou, “Nanotechnology 18 (2007) 275606. [4] R. N. Goyal, D. Kaur & A. K. Pandey, “Growth and characterization of iron oxide nanocrystalline thin films via low-cost ultrasonic spray pyrol- ysis”, Materials Chemistry and Physics 116 (2009) 638. [5] M. Ritu, “A Simple and Effective Method of the Synthesis of Nanosized Fe2O3 particles”, IOSR Journal of Applied Chemistry 4 (2013) 41. [6] M. Aronniemi, J. Lahtinen & P. Hautojarvi, “Characterization of iron ox- ide thin films”, Surf. Interface Anal. 36 (2004) 1004. [7] Z. Hubicka, S. Kment, J. Olejnı́cek, M. Cada, T. Kubart, M. Brunclikov, P. Ksirov, P. Adámek & Z. Remes , “Deposition of hematite Fe2O3 thin film by DC pulsed magnetron and DC pulsed hollow cathode sputtering system”, Thin Solid Films 549 (2013) 184. [8] SPRINGER Encyclopedia of Soil Science, Edited by Chesworth W. XXVI (2008) 369. [9] F.H. Fermin, D. Aragon, J. Ardisson, Juan C.R. Aquino, I. Gonzalez, W. A. Macedo, A.H. Coaquira, J. Mantilla, S. W. da Silva, & P. C. Morais, “Effect of the thickness reduction on the structural, surface and magnetic properties of α-Fe2O3 thin films”, Thin Solid Films 607 (2016) 54. [10] M. R. Belkhedkar, & A. U. Ubale, “Preparation and Characterization of Nanocrystalline α- Fe2O3 Thin Films Grown by Successive Ionic Layer Adsorption and Reaction Method”, International Journal of Materials and Chemistry 4 (2014) 109. [11] L. A. Marusak, R. Messier, W. B. White, J. Phys. Chem. Solids 41 (1980) 981. [12] N. Beermann, L. Vayssieres, S. E. Lindquist & A. Hagfeldt, J. Elec- trochem. Soc. 147 (2000) 2456. [13] A. Kleiman-Shwarsctein, Y. S. Hu, A. J. Forman, G. D. Stucky, & E. W.McFarland, J. Phys. Chem. C 112 (2008) 15900. [14] N. C. Debnath, A. B. Anderson, J. Electrochem. Soc. 129 (1982) 2169. [15] K. Sivula, F. Le Formal, & M. Gratzel, “Solar Water Splitting: Progress Using Hematite (α-Fe2O3) Photoelectrodes”, ChemSusChem 4 (2011) 432. [16] R. N. Goyal, D. Kaur, & A. K. Pandey, “Growth and characterization of iron oxide nanocrystalline thin films via low-cost ultrasonic spray pyrol- ysis”, Materials Chemistry and Physics 116 (2009) 638. [17] M. Mishra & D.-M. Chun, “α-Fe2O3 as a Photocatalytic material: A Review”, Applied Catalysis A, General (2015) 023. [18] Z. Zhou, Q. Zhang, J. Sun, B. He, J. Guo, Q., Li, C. Li, L. Xie, & Ya- gang Yao, “Metal-Organic Framework Derived Spindle-like Carbon In- corporated α-Fe2O3 Grown on Carbon Nanotube Fiber as Anodes for High-Performance Wearable Asymmetric Supercapacitors”, ACS Nano 12 (2018) 9333. [19] S. Gahlawata, N. Rashida & P. P. Ingole, “n-Type Cu2O/ α- Fe2O3 Het- erojunctions by Electrochemical Deposition: Tuning of Cu2O Thickness for Maximum Photoelectrochemical Performance”, Z. Phys. Chem. 232 (2018) 1551. [20] H. Magnan, D. Stanescu, M. Rioult, E. Fonda, & A. Barbier, Enhanced photoanode properties of epitaxial Ti doped a- Fe2O3 (0001) thin films, Applied Physics Letters 101 133908 (2012). [21] L. Wang, C-Y. Lee, A. Mazare, K. Lee, J. Muller, E. Spiecker & P. Schmuki, “Enhancing the Water Splitting Efficiency of Sn-Doped Hematite Nanoflakes by Flame Annealing”, Chem. Eur. J. 20 (2014) 88. [22] A. Annamalai , P, S. Shinde, T. H. Jeon, H. H. Lee , H. G. Kim, W. Choi & J. S. Jang, “Fabrication of superior α-Fe2O3 nanorod photoan- odes through ex-situ Sn-doping for solar water splitting”, Solar Energy Materials & Solar Cells 144 (2016) 247. [23] I. Cesar, K. Sivula, A. Kay, R. Zboril & M. Gratzel, “Influence of Fea- ture Size, Film Thickness, and Silicon Doping on the Performance of Nanostructured Hematite Photoanodes for Solar Water Splitting”, J. Phys. Chem. C 113 (2009) 772. [24] P. Sharma, P. Kumar, D. Deva, R. Shrivastav, S. Dass & V. R. Satsangi, “Nanostructured Zn- Fe2O3 thin film modified by Fe-TiO2 for photoelec- trochemical generation of hydrogen”, International Journal of Hydrogen Energy 35 (2010) 10883. [25] C. Jorand Sartoretti, M. Ulmann, B.D. Alexander, J. Augustynski & A. Weidenkaff, “Photoelectrochemical oxidation of water at transparent fer- ric oxide film electrodes”, Chemical Physics Letters 376 (2003) 194. [26] I. K. Kim, Y. G. Kim & T. Y. Park, “Preparation and Characterization on Thin Films of Doped Iron Oxide Semiconductive Electrodes”, Analytical Sciences 7 (1991) 222. [27] S. Krehula, G. Stefanic, K. Zadro, L. K. Krehula, M. Marcius, S. Music, “Synthesis and properties of iridium-doped hematite (a-Fe2O3)”, Journal of Alloys and Compounds 545 (2012) 200. [28] L. Wang, C-Y Lee & P. Schmuki, “Ti and Sn co-doped anodic α-Fe2O3 films for efficient water splitting”, Electrochemistry Communications 30 (2013) 21. [29] C. X. Kronawitter, I. Zegkinoglou, S.-H. Shen, P. Liao, I. S. Cho, O. Zandi, Y.-S. Liu, K. Lashgari, G. Westin, J.-H. Guo, F. J. Himpsel, E. A. Carter, X. L. Zheng, T. W. Hamann, B. E. Koel, S. S. Mao & L. Vayssieres, “Titanium incorporation into hematite photoelectrodes: the- oretical considerations and experimental observations”, Energy Environ. Sci. 7 (2014) 3100. [30] C-Y Lee, L. Wang, Y. Kado, R. Kirchgeorg & P. Schmuki, “Si-doped Fe2O3 nanotubular/nanoporous layers for enhanced photoelectrochemical water splitting”, Electrochemistry Communications 34 (2013) 308. [31] P. Kumar, P. Sharma, R. Shrivastav, S. Dass & V. R. Satsangi, “Elec- trodeposited zirconium-doped α- Fe2O3 thin film for photoelectrochem- ical water splitting, International Journal of Hydrogen Energy 36 (2011) 2777. [32] E. L. Tsege, T. Sh. Atabaev, M. A. Hossain, D. Lee, H-K. Kim & Y- H. Hwang, “Cu-doped flower-like hematite nanostructures for efficient water splitting application”, Journal of Physics and Chemistry of Solids 98 (2016) 283. [33] V. R. Satsangi, S. Kumaria, A. P. Singh, R. Shrivastav & S. Dass, “Nanos- tructured hematite for photoelectrochemical generation of hydrogen”, In- ternational Journal of Hydrogen Energy 33 (2008) 312. [34] Vibha R. Satsangi, Saroj Kumari, A. P. Singh, R. Shrivastav & S. Dass, “Nanostructured hematite for photoelectrochemical generation of hydro- gen”, International Journal of Hydrogen Energy 33 (2008) 318. [35] V. Martis, R. Oldman, R. Anderson, M. Fowles, T. Hyde, R. Smith, S. Nikitenko, W. Bras & G. Sankar, “Structure and speciation of chromium ions in chromium doped Fe2O3 catalysts”, Phys. Chem. Chem. Phys. 15 (2013) 168. [36] K. V. Siva & R. N. Bhowmik, “Structural, magnetic and magneto-electric properties of Cr doped α-Fe2O3”, AIP Conference Proceedings 2115 (2019) 030491. [37] G. Goyal, A. Dogra, S. Rayaprol, S.D. Kaushik, V. Siruguri, H. Kis- han, “Structural and magnetization studies on nanoparticles of Nd doped Fe2O3”, Materials Chemistry and Physics 134 (2012) 133. [38] I. Kuryliszyn-Kudelskaa, B. Hadzicb, D. Siberac, L. Kilanskia , N. Romcevicb , M. Romcevicb, U. Narkiewiczc and W. Dobrowolskia, “Nanocrystalline ZnO Doped with Fe2O3 — Magnetic and Structural Properties”, Acta Physica Polonica A 119 (2011) 689. [39] F. S. Freyria, G. Barrera, P. Tiberto, E. Belluso, D. Levy, G. Saracco, P. Allia, E. Garrone, B. Bonelli, “Eu-doped α- Fe2O3 nanoparticles with modified magnetic properties”, Journal of Solid State Chemistry 201 (2013) 311. [40] Z., P., Wand, N., Hu, W., S. Kormarmeni, “Anode electrodeposition of 3D mesoporous Fe2O3 nonosheets on carbon fabric for flexible solid state asymmetric supercapacitor”. Ceramics international 45 (2019) 10420. [41] V.D. Nithya, N. Sabari Arul, “Review on α-Fe2O3 based negative elec- trode for high performance supercapacitors”, Journal of Power Sources 327 (2016) 297. [42] K. Tang, H. Ma, Y. Tian, Z. Liu, H. Jin, S. Hou, K. Zhou, X. Tian, “3D printed hybrid-dimensional electrodes for flexible micro-supercapacitors with superior electrochemical behaviours”, Virtual and Physical Proto- typing 15 (2020) 511. [43] Y-J. Gu, W. Wen, S. Zheng, J-M. Wu, “Rapid synthesis of high-areal- capacitance ultrathin hexagon Fe2O3 nanoplates on carbon cloth via a versatile molten salt method”, Mater. Chem. Front. 4 (2020) 2744. [44] F. Han, J. Xu, J. Zhou, J. Tang, W. Tang, “Oxygen vacancy-engineered Fe2O3 nanoarrays as free-standing electrodes for flexible asymmetric su- percapacitors”, Nanoscale 11 (2019) 12477. [45] C. Liu, Q. Li, J. Cao, Q. Zhang, P. Man, Z. Zhou, C. Li, Y. Yao, “Su- perstructured α-Fe2O3 nanorods as novel binder-free anodes for high- 12 Fasasi et al. / J. Nig. Soc. Phys. Sci. 5 (2023) 1180 13 performing fiber-shaped Ni/Fe battery”, Science Bulletin 65 (2020) 812. [46] F. Li, Y-L. Liu, G-G. Wang, H-Y. Zhang, B. Zhang, G-Z. Li, Z-P. Wu, “Le-Yang Dang, Jie-Cai Han Few-layered Ti3C2Tx Menes coupled with Fe2O3 nanorod arrays grown on carbon cloth as anodes for flexible asymmetric supercapacitors”, J. Mater. Chem. A. 7 (2019) 22631. [47] Q Wang, C. Guo, J. He, S. Yang, Z. Liu, Q. Wang, “Fe2O3/C-modified Si nanoparticles as anode material for high-performance lithium-ion batter- ies”, Journal of Alloys and Compounds 30 (2019) 284. [48] K Le, M. Gao, D. Xu, Z. Wang, G. Wang, W. Liu, F. Wang, J. Liu, “Polypyrrole-coated Fe2O3 nanotubes constructed from nanoneedles as high-performance anodes for aqueous asymmetric supercapacitors”, Dal- ton Trans. 49 (2020) 9709. [49] X.-F, Lu, X-Y. Chen, W. Zhou, Y-X. Tong, G-R. Li, “α-Fe2O3 PANI Core-Shell Nanowire Arrays as Negative Electrodes for Asymmetric Su- percapacitors”, ACS Appl. Mater. Interfaces 7 (2015) 14850. [50] Y. Luo, J. Luo, J. Jiang, W. Zhou, H. Yang, X. Qi, H. Zhang, H. J. Fan, Denis Y. W. Yu, C. M. Li & T. Yu, “Seed-assisted synthesis of highly ordered TiO2@α-Fe2O3 core/shell arrays on carbon textiles for lithium-ion battery applications”, Energy Environ. Sci. 5 (2012) 6566. [51] M, Yang, S, Z. Qing, Y. Cuang, G. Wang, S., Teng, Fei, L. Guohua & A. Zhaoquan, “Cu-Doped α-Fe2O3 Microspheres as Anode Materials for Lithium-Ion Batteries”, Journal of Nanoscience and Nanotechnology 16 (2018) 4296. [52] F. A.Harraz, A. A. Ismail, S. A. Al-Sayari & A. Al-Hajry, “Novel Fe2O3/Polypyrrole Nanocomposite with Enhanced Photocatalytic Perfor- mance”, Journal of Photochemistry and Photobiology A: Chemistry 299 (2015) 18. [53] J-C. Wu, W-M. Yan, C-T. Wang, C-H. Wang, Y-H. Pai, K-C. Wang, Y- M. Chen, T-H. Lan & S. Thangavel, “Treatment of Oily Wastewater by the Optimization of Fe2O3 Calcination Temperatures in Innovative Bio- Electron-Fenton Microbial Fuel Cells”, Energies 11 (2018) 565. [54] T. K. Singh, S. A. Bansal & S. Kumar, “Graphene oxide (GO)/Copper doped Hematite (α-Fe2O3) nanoparticles for organic pollutants degrada- tion applications at room temperature and neutral pH, Materials Research Express 6 (2019) 115026. [55] H. Feng, L. Tang, J. Tang, G. Zeng, H. Dong, Y. Deng, L. Wang, Y. Liu, X. Ren & Y. Zhou, “Cu-Doped Fe2O3 core-shell nanoparticle shifted oxygen reduction pathway for high-efficiency arsenic removal in smelting wastewater”, Environ. Sci.: Nano 5 (2018) 1595. [56] S. S. Chahal, A. Kumar & P. Kumar, “Zn Doped α- Fe2O3: An Effi- cient Material for UV Driven Photocatalysis and Electrical Conductivity”, Crystals 273 (2020) 18. [57] S. Upasen, “Activated carbon-doped with iron oxide nanoparticles (α- Fe2O3 NPs) preparation: particle size, shape, and impurity”, International Journal of ChemTech Research 11 (2018) 33. [58] O.M. Lemine I. Ghiloufi, M. Bououdina, L. Khezami, M. O. M’hamed, A.T. Hassan, “Nanocrystalline Ni-doped a-Fe2O3 for adsorption of met- als from aqueous solution”, Journal of Alloys and Compounds 588 (2014) 592. [59] A. A. Ismail, “Synthesis and characterization of Y2O3/ Fe2O3/TiO2 nanoparticles by sol-gel method”. Applied Catalysis B: Environmental 58 (2005) 115. [60] J. Ouyang, Z. Zhao, S.L. Sui & H. Yang, “Degradation of Congo Red Dye by a Fe2O3@CeO2-ZrO2/Palygorskite Composite Catalyst: Synergetic Effects of Fe2O3”, Journal of Colloid and Interface Science 539 (2019) 135. [61] G. Picasso, M.R. Sun Kou, O. Vargasmachuca, J. Rojas, C. Zavala, A. Lopez & S. Irusta, “Sensors based on porous Pd-doped hematite (α- Fe2O3) for LPG detection”, Microporous and Mesoporous Materials 185 (2014) 85. [62] C. Cantalini, H.T. Sun, M. Faccio, G. Ferri & M. Pelino, “Niobium-doped a-Fe203 semiconductor ceramic sensors for the measurement of nitric ox- ide gases”, Sensors and Actuators B 24-25 (1995) 671. [63] P. Sun, C. Wang, X. Zhou, P. Cheng, K. Shimanoe, G. Lu, N. Yamazoe, “Cu-doped α-Fe2O3 hierarchical microcubes: Synthesis and gas sensing properties”, Sensors and Actuators B: Chemical 193 (2014) 622. [64] N. Funazaki, A. Hemmi, S. Ito, Y. Asano, S. Yamashita, T. Kobayashi & M. Haruta, “Development of carbon monoxide detector doped α-Fe2O3”, Sensors and Actuators B 13-14 (1993) 538. [65] A. M. Schultz, Y. Zhu, S. A. Bojarski, G. S. Rohrer & P. A. Salvador, “Eutaxial growth of hematite Fe2O3 films on perovskite SrTiO3 poly- crystalline substrates”, Thin Solid Films 548 (2013) 224. [66] M. Su, C. He & K. Shih, “Facile synthesis of morphology and size- controlled α-Fe2O3 and Fe3O4 nano-and microstructures by hydrother- mal/solvothermal process: The roles of reaction medium and urea dose”, Ceramics International 42 (2016) 14793. [67] J. A. Glasscock, P. R. F. Barnes, I. C. Plumb, A. Bendavid & P. J. Martin, “Structural, optical and electrical properties of undoped polycrystalline hematite thin films produced using filtered arc deposition”, Thin Solid Films 516 (2008) 1716. [68] M. N. Batin & V. Popescu, “The influence of deposition time on optical properties of iron oxide films grown on glass substrate by Chemical Bath Deposition”, Optoelectronics and Advanced Materials – Rapid Commu- nications 6 (2012) 729. [69] A. Lassoued, M. Saber Lassoued, B. Dkhil, A. Gadris & S. Ammar, “Structural, optical and morphological characterization of Cu-doped α- Fe2O3 nanoparticles synthesized through co-precipitation technique”, Journal of Molecular Structure 1148 (2017) 281. [70] C. Aydin, Sh. A. Mansour, Z. A. Alahmed & F. Yakuphanoglu, “Struc- tural and optical characterization of sol–gel derived boron doped Fe2O3 nanostructured films”, J. Sol-Gel Sci Technol. 62 (2012) 397. [71] A. Y. Fasasi, E. Osagie, D. Pelemo, E. Obiajunwa, E. Ajenifuja, J. Ajao, G. Osinkolu, W. O. Makinde & A. E. Adeoye, “Effect of Precursor Sol- vents on the Optical Properties of Copper Oxide Thin Films Deposited Using Spray Pyrolysis for Optoelectronic Applications”, American Jour- nal of Materials Synthesis and Processing 3 (2018) 22. [72] A.S. Hassanien & A. A. Akl, “Influence of composition on opti- cal and dispersion parameters of thermally evaporated non-crystalline Cd50S50 xSex thin films”, Journal of Alloys and Compounds 648 (2015) 290. [73] A.S. Hassanien & A. A. Akl, “Effect of Se addition on optical and elec- trical properties of chalcogenide CdSe thin films”, Superlattices and Mi- crostructures 89 (2016) 169. [74] J. Tauc & A. Menth, “States in the gap”, J Non-Crystalline Solids 8-10 (1972) 585. [75] N.F. Mott & E.A. Davis, Electron processes in non-crystalline materials, Clarendon, Oxford, 1979. [76] E.N. Economou & M. H. Cohen, “Anderson’s theory of localization and the Mott-CFO model”, Material Research Bulletin 8 (1970) 590. [77] “Optical Properties of Condensed Matter and Applications”, Jai Singh (eds.) Wiley Series in Materials foe Electronics and Optoelectronic Ap- plications, John Wiley and Sons Ltd. West Sussex, PO19 8SQ, England, 2006. [78] J. Melsheimer & D. Ziegler, Band gap energy and Urbach tail studies of amorphous, partially crystalline and polycrystalline tin dioxide, Thin Solid Films 129 (1985) 47. [79] S.J. Ikhmayies & R.N. Ahmad-Bitar, “A study of the optical bandgap energy and Urbach tail of spray-deposited CdS:In thin films”, Journal of Materials Research and Technology 2 (2013) 227. [80] K.A. Aly, A.A. Elnaeim, M. Uosif & O. Abdel-Rahim, “Optical proper- ties of Ge–As–Te thin films”, Physica B: Condensed Matter 406 (2011) 4232. [81] S. Ikhmayies & R. Ahmad-Bitar, “Thickness dependence of the bandgap energy and Urbach tail for CdS thin films prepared by vacuum evapora- tion, in: Proceedings of the World renewable energy congress and exhibi- tion XI (2010) 979. [82] S.H. Wemple & M. Di-Domenico, “Behaviour of the electronic dielectric constant in covalent and ionic materials”, Phys. Rev. B 3 (1971) 1350. [83] S. H. Wemple, “Refractive-index behaviour of amorphous semiconduc- tors and glasses”, Phys. Rev. B 7 (1973) 3776. [84] A. S. Hassanien, “Studies on dielectric properties, opto-electrical pa- rameters and electronic polarizability of thermally evaporated amorphous Cd50S50-xSex thin films”, Journal of Alloys and Compounds 671 (2016) 578. [85] H. Tichá & L. Tichý, “Semiempirical relation between non-linear suscep- tibility (refractive index), linear refractive index and optical gap and its application to amorphous chalcogenides”, Journal of Optoelectronics and Advanced Materials 2 (2002) 386. 13