Influence of Gd content on structural, electronic, thermoelectric, and optical properties of WO3

WO3-based semiconductor materials are optimistic competitors for modern electronic devices because of their outstanding electronic and optical properties. Simulations on pure and Gd-doped WO3 compositions were executed using Tran and Blaha modified Becke–Johnson approximation. Experimentally, thin films of these compositions were prepared using the chemically derived technique. X-ray diffraction spectra of thin films exhibited cubic structure having space group 221-Pm-3m in all compositions. Field emission scanning electron micrographs reveal the uniform growth of thin films with rod-like compact morphology. The density of states spectra for electronic properties demonstrate the main contribution of W-d and O-p for pure WO3 with p-d hybridization while Gd containing composition provides an additional prominent contribution from f-orbital. Band structure shows an indirect transition for WO3 and band gap values were observed as 1.73 eV which decreased with increment of Gd content. A significant change in thermoelectric parameters was observed with an increment of temperature and Gd doping. The maximum value of the refractive index was observed as 3.02 in the visible energy regime and tends to decrease in Gd containing compositions. The experimentally obtained maximum dielectric constant was observed as 7.89 for pure WO3 and decreased to 4.58 for maximum Gd containing composition. Optical parameters like extinction, absorption coefficient, and optical conductivity show a sharp increment in visible energy region which make these compositions favorable for photovoltaic and optoelectronic applications. The experimentally obtained optical parameters are found in good agreement with simulated results obtained through TB-mBJ approximation.


Introduction
Tungsten oxide (WO 3 ) exhibited excellent conductivity and high electron hall mobility which considered it a promising candidate for optoelectronic applications [1][2][3][4][5].WO 3 thin films attracted huge interest in the last decade because of potential applications.Thin film works were mainly focused on advanced strategies in the development of WO 3 -based devices for photovoltaic and optoelectronic applications [6,7].These thin films have been used in electrochromic devices, displays, and smart windows [8,9].It is an n-type semiconductor having a wide electronic band gap reported in the range of 2.6-3 eV [10][11][12][13].The band gap of this material significantly plays a crucial role in both fundamental and applied physics.However, literature related to the band gap is somewhat confusing as below 3 eV values of the band gap were obtained by assuming an indirect transition [14].Many attempts have been made for the deposition of WO 3 thin films doped with different metallic ions such as Cr, Ru, CuO, Ti, Tb 3+ , Cd, In, Sn, and Eu 3+ using different fabrication techniques like facile chemical method, template-free hydrothermal method, radio frequency (RF) magnetron sputtering technique, and chemically derived simple low cost spin coating [15][16][17][18][19][20][21][22].
The Tran and Blaha (TB) modified Becke Johnson (mBJ) exchange potential approximation was used to analyze the electronic and structural properties.On the other hand generalized gradient approximation (GGA) and local density approximation (LDA) are significantly successful to compute structural characteristics [23].Yet these are unable to provide comparable results by simulations with experimental techniques.Hence there are more approximations needed that can reproduce theoretical simulations the same as the experimental results.Green's function (GW) approximation is an appropriate approach to studying band gap but the computing cost is much higher as reported in the literature [24].However, Tran and Blaha presented an effective, highly precise, accurate, and inexpensive approach to studying the band gaps [25].
In the current study, the physical properties of WO 3 thin films were studied by Gd doping as rare earth elements significantly improve the structural, electronic, and optical properties.The simulations were performed on pure and Gd-doped WO 3 compositions using TB-mBJ approximation in well-known Wien2K code.Thin films of the same compositions were fabricated using the chemically derived spin coating method for experimental investigations.The purpose of this work is a comparative study between experimental parameters of structural, electronic, thermoelectric, and optical properties with simulated investigations for a better understanding of the responses to attain an impressive outcome regarding photovoltaic and optoelectronic applications.

Computational and experimental methods
2.1.Computational details TB-mBJ approximation is an accurate technique used in the well-known Wien2K code for materials simulations.This approximation was employed in this work for the investigation of pure and Gd-doped WO 3 thin films.This approximation provides surprisingly very accurate results in comparison to optical properties and band gap obtained with experimental data for many semiconductors and insulators [26].The cubic lattice of WO 3 was selected for simulations with lattice constant a = b = c = 3.81 Å.The different supercell configurations were used for 5.55, 8.33, and 12.5 at% Gd doping in WO 3 structure.The maximum value of k vector was selected under spherical symmetric potential while the values of l max and RMT x K max were adjusted at 10 and 7.The energy and charge convergence values were set at 10 −2 , and the value of Gaussian smearing was adjusted at 0.1 eV for self-criterion consistency.The thermoelectric parameters like the Seebeck coefficient were investigated using Boltztrap software embedded in Wien2k-code.

Experimental methods
Thin films of similar compositions as simulated through software were experimentally fabricated using the chemically derived spin coating method.The initial solutions stoichiometric amounts were prepared using Tungsten hexachloride [WCl 6 ] and Gadolinium nitrate hexahydrate [Gd(NO 3 ) 3 •6H 2 O] obtained from Sigma-Aldrich as starting raw precursors in .anhydrousethyl alcohol.The soda lime glass slides (20 × 20 mm) were cleaned with Isopropyl Alcohol (IPA) and methanol for 10 min each.The calculated amount of constituents was constantly stirred and heated at 100 °C to get appropriate viscous solutions.These prepared viscous solutions were spin-coated with a spinning speed of 3000 rpm for 45 seconds on well-cleaned glass substrates.Now to get the best results for standardized morphology and cubic crystalline phase, these glass-coated slides were shifted to a muffle furnace and annealed for 4 h at 400 °C.The thickness of the thin films was observed as 300 ± 10 nm for all compositions.The phase purity and crystalline nature of prepared thin films were analyzed using x-ray diffraction (Panalytical-X'Pert Pro Multipurpose Diffractometer).The XRD was operated with 40 kV and 40 mA voltage and current values, respectively.FEI Nova NanoSEM 450 field emission scanning electron microscope (FESEM) equipped with Oxford INCA X'ACT EDX was employed to characterize the thin films for morphology and elemental compositions.FESEM micrographs were obtained at 10 kV electron beam energy using through lens detector under charge neutralization mode.The working distance was adjusted at approximately 5 mm to get the maximum signal at the detector.The optical properties of the thin film were acquired using Woolamson Alpha-SE spectroscopic ellipsometer.

Structural studies
Crystal structure and phase purity of prepared thin films were investigated using x-ray diffraction and XRD patterns are presented in figure 1.The XRD spectra of thin films exhibited a cubic structure having space group 221-Pm-3m in all compositions which can be correlated with standard JCPD-card 00-041-0905 of WO 3 .Thin films grown with chemical methods sometimes provide such noisy patterns.XRD pattern of pure WO 3 thin films showed two peaks at 2θ values 23.22°and 35.81°havingMiller indices (100) and (110), respectively, those were reported in the literature as well [27,28].In case of thin films, only one or few peaks appeared associated with prominent planes, unlike the bulk samples.These peaks were slightly shifted to lower angles and exhibited some broadening for Gd-doped compositions.This shift arises due to variance in ionic radii of Gd 3+ (0.0938 nm) and W 6+ (0.060 nm) ions.This difference creates the lattice distortions and expansion in lattice.The similar trend was observed by Liu et al, in recently reported work [29].No other peak appeared associated with any other phase or impurity.This reveals the well crystalline stability and phase purity of the compositions upon doping of Gd content in structure.The difference in ionic radii of host W and dopant Gd elements is responsible for the shift and broadening of XRD peaks in spectra.The average crystallite size was estimated using the well known Debye-Scherrer formula [30] D , k cos = l b q Where k is the shape factor constant, λ is the wavelength of x-rays, β is the full width at half maximum, and θ is the angle of diffraction.The dislocation density ( ), d and micro-strain (e) in thin films can be calculated using the relations [30]  and

Calculated
results in table 2. The values of calculated crystallite size, lattice strain, and dislocation density for all compositions are presented in table 1.The crstallite size was found to decrease with incorporation of Gd content in structure which is attributed to the lattice distortions as shown by the increasing trend of lattice starin.

Morphology and compositional analysis
Field emission scanning electron microscopy and energy dispersive x-ray spectroscopy analysis were executed to find the morphological and elemental compositions of pure and Gd-doped WO 3 thin films.Figure 2 shows the  FESEM micrographs of thin films obtained at ×25k magnifications.Pure WO 3 thin films presented in figure 2(a) contained the uniform and evenly distributed rod-like morphology.These rods are oriented in different directions.Thin films grown with some chemically derived method often produce such features which are not sometimes continuous.The shape and size of these rods slightly changed in the morphology of Gd containing compositions shown in figures 2(b)-(d).Some small particles and agglomerations were also observed in these compositions.However, the homogeneity of thin films remained intact with some changes in distribution as rod-like morphology retained by the samples doped with Gd. Figure 3 presents the elemental composition analysis obtained by EDX spectra for both pure and doped WO 3 thin films.The EDX spectra illustrate the incorporation of Gd-content in thin films with nominal increasing contents as the Gd peak increased with the increment of its content.These spectra revealed the purity of thin films regarding elemental contents as no other impurity element peak was detected in spectra.The elemental contents obtained through EDX analysis for all compositions are presented in table 2.

Band structure and electronic properties
The band structure is an excellent way to explore the electronic behavior and band gap of materials [31].The band structure of pure and Gd-doped WO 3 was studied by plotting the curves obtained using TB-mBJ approximation as displayed in figure 4. The Fermi level E f is demonstrated by a dotted line at 0 eV.The valence band lies below the Fermi level while above it is the conduction band.The gap between the valence band and the conduction band can predict the nature of the semiconducting material.The gap of pure WO 3 tends to decrease with Gd-doping content as shown in figure 4 which is attributed to the increment in conductivity.There is a difference in dopant Gd and host W valence states which is attributed to the defects and oxygen vacancies in the structure.The Gd content in WO 3 produced degenerate semiconductors which were responsible for the decrease in band gap and enhanced conductivity.The simulated energy band value for pure WO 3 is approximately 1.7 eV.The total density of states (TDOS) and projected density of states (PDOS) were plotted as a function of energy and presented in figures 5, and 6, respectively.The valence band filled by maxima in TDOS spectra is in the energy range of −1.6 eV to −3.1 eV.A similar TDOS spectral output was observed in the reported literature [32].From the figure, it is also observed that pure WO 3 showed the semiconducting nature of the material with an indirect transition.However, a direct transition was also reported in the literature with a similar type of material with a direct band gap of 2.8 eV [33].As the value Gd content increased in WO 3 , the maxima of TDOS The pure WO 3 reveals the p-d hybridization of the d-orbital of W and p-orbital of O while the f-orbital contribution is prominent from the Gd atom and overlaps at the fermi level in Gd-doped WO 3 compositions.

Thermoelectric properties
The thermoelectric properties were studied by obtaining the various parameters such as See-beck coefficient, electrical conductivity, thermal conductivity, and specific heat capacity of pure and Gd-doped WO 3 compositions as presented in figure 7.These properties are strongly depending on band structure and Boltzmann transport equation; The symbols T and μ represent temperature and doping level which are mainly influenced the electrical conductivity.Here f(u) is the Fermi distribution function while both chemical potential and volume are symbolized by ε.The relation between electrical conductivity and the Seebeck coefficient is presented in the following equation;  The thermal conductivity is expressed as; The above theoretical and mathematical expressions are all reported in previous literature [34].The trend of the Seebeck coefficient versus temperature shows parabolic curves for all compositions as presented in figure 7(a).The values of the Seebeck coefficient were enhanced first with the increment in temperature up to 250 °Ċ and then suddenly dropped at the higher values of temperature.The reason behind this parabolic trend is that the effect of minority charge carriers at high temperatures can't be ignored.The values of the Seebeck coefficient were observed to increase with the doping of Gd content.The maximum value of the Seebeck coefficient was observed as ≈1.23 μVK −1 for pure and ≈2.23 μVK −1 for maximum doping content of Gd.
Figure 7(b) shows the trend of electrical conductivity (σ) versus temperature for pure and doped WO 3 compositions.The value of σ was slightly decreased as the temperature increased while the values were significantly increased with the increment in Gd doping concentration.The enhancement of electrical conductivity with the increase in Gd content is associated with the additive-free charge carriers which are considered favorable for good thermoelectric materials.The temperature-dependent electrical conductivity gave the idea that the flow of electrons and lattice vibrations are possible due to heat conduction in a material [34].The highest values of σ were observed at the lowest temperatures as ≈1.67 × 10 19 S m −1 for pure WO 3 and ≈5.91 × 10 19 S m −1 for maximum content of Gd containing composition.The decrease in electrical conductivity at the highest temperatures revealed the rise in lattice distortions due to heat effects.
Figure 7(c) shows the trend of thermal conductivity versus temperature acquired through the Boltztrap code.The thermal conductivity was observed to increase with temperature as well as with an increment of Gd content in WO 3 .This enhanced trend is associated with the significant increase in charge carriers due to Gd doping content as predicted in electronic properties while with increment of temperature flow of charge carriers were improved.The maximum values of thermal conductivity are hence observed at highest values of temperatures for all compositions.The highest values of thermal conductivity for pure WO3 were observed as ≈3.39 × 10 14 W.(mK) −1 and ≈7.73 × 10 14 W.(mK) −1 for the highest Gd containing compositions.

Optical properties
The optoelectronic response of any material can be observed by refractive index and reflection.The refractive index differs by changing the medium and thickness of thin films.It depends on the divergence of EM-radiations from the surface of these thin films.The refractive index curves for pure and Gd-doped WO 3 thin films were attained through simulations and experiments as shown in figures 8(a) and 9(a).Static values of n were observed through simulations for pure WO 3 as ≈2.07, and ≈2.20, ≈1.95, ≈2.46 for 5.55%, 8.33%, and 12.5% for Gddoped WO 3 .The highest value of n was calculated as ≈3.04 for pure WO 3 and ≈2.65 for 5.55%, ≈2.67 for 8.33%, ≈2.53 for 12.5% at the highest values of photon energy, respectively.From figure 9(a), it can be observed that experimentally obtained values of refractive index for pure and Gd-doped WO 3 compositions followed a similar trend as simulated results.
The extinction coefficient (k) depends significantly on the incident absorption capability of material and complex refraction function.It can be mathematically derived as; Here α is symbolized for absorption coefficient.Figures 8(b) and 9(b) describe trends of simulated and experimental curves of extinction coefficient (k) versus photon energy for pure and Gd-doped WO 3 thin films.It can be observed in these results the value of k increased with the increment of photon energy and spotted very sharp excitonic peaks in the range between 3-4 eV.Experimental curves also revealed the same results in the identical energy ranges as shown in figure 9(b).Further, this excitonic peak idea can be described better with the support of Mie's theory [35].This theory stated that full-width half maxima (FWHM) are linked with excitonic peaks and depend upon grain or particle size and wavelength of incident light.These composition studies in this work can play a central role in photovoltaic applications because k values are highly raised in visible photon energy regions.
Optical conductivity is an important parameter and can be formulated as [36]; The simulated and experimentally obtained optical conductivity curves for pure and Gd-doped WO 3 composition are shown in figures 8(c) and 9(c).These parameters gave the idea about the stability of the material for optoelectronic applications.Simulated results shown in figure 8(c) revealed the highest values in the photon energy range of 3.5-4 eV in the highest photon energy region.Due to the good optical response of studied compositions, these are demonstrated as suitable candidates for optoelectronic applications.The experimentally obtained curves exposed some differences by enhancement of Gd concentration and photon energy in comparison to simulated results due to an increase in the mobility of charge carriers.
The other essential parameter is the absorption coefficient which describes the response of material when light is exposed to it.Mathematically, it can be calculated by real and imaginary parts of the dielectric constant.It is symbolized as ( ) a w and can be expressed with the following relation [37]; a w e w e w e w = + -Figure 8(d) shows the optical absorption coefficient versus photon energy obtained using simulations which narrate that by increasing photon energy the absorption coefficient values also increase and attained the highest value at the highest photon energies.The experimental curves show a twin trend in the visible regime for this parameter as presented in figure 9(d).The absorption edges appear in curves, especially in the high energy regimes.While lower values were observed in the low-energy regions which reveal that these compositions can act as good transmitter.
Reflectivity can be defined in terms of the ratio between incident and reflected radiations.It depends upon the surface morphology, angle of incident, and type of polarized light.It describes how a material responds optically and can be formulated as;  Figures 8(e) and 9(e) show the trend of simulated and experimentally obtained curves for reflectivity as a function of photon energy for pure and Gd-doped WO 3 thin films.The values of reflectivity were found to increase with the increase of photon energy and attained maximum values in the higher energy regimes.While Gd-doped WO 3 material showed a slight variable trend as compared to pure host materials due to the photon interactions with the surface of thin films.
The Real epsilon (ε r ) describes the propagation of light through the material.In terms of Kramer-Kroning Transformations (KKT), it can be mathematically described as [34]; and 9(f) present simulated and experimental curves of ε r versus photon energy for both pure and Gd-doped WO 3 thin films.These results convey the same trend as the refractive index.Both curves of Gd-doped and pure WO 3 thin films describe that by increment in photon energy, ε r value first increased and then decreased accordingly.Further, pure WO 3 presents the highest value of ε r in the curve.For pure WO 3 , the maximum dielectric constant value was observed as ≈7.89, while it was observed as ≈6.76, ≈6.03, and ≈4.58 for 5.55%, 8.33%, and 12.5% Gd-doped compositions, respectively.The experimental trend of the dielectric constant also seems identical and comparable with simulated results.The comparison of the simulated and experimental results with literature are presented on table 3.
The Tauc equation is used to determine the optical band gaps using absorption coefficient data [38]; In the above equation, α is the absorption coefficient, A is the material constant, E g, is the optical band gap, and hν represents photon energy, the value of n shows optical transition, n = 2 for direct band gap, and 1/2 for  indirect transition.WO 3 has an indirect energy bandgap.So, the energy bandgap of all the prepared samples is investigated by plotting (αhν) 1/2 as a function of the energy of the photon.The values of optical energy bandgap for the prepared thin films are found to be 2.27, 1.93, 1.81, and 1.71 eV for Pure WO 3 , 5.55%, 8.33%, and 12.5% Gd doped WO 3 respectively, as shown in figure 10.This trend showed that band gap of doped thin films decreased with the increase of doping content attributed to the presence of new localized energy states.It is observed from the plot that after the inclusion of Gd as a dopant into the WO 3 host matrix it turns into the degenerate semiconductor which reflects the metallic behavior after the addition of Gd.This is also confirmed by our theoretically obtained results.

Conclusion
Thin films of Gd-doped WO 3 compositions were prepared in phase pure crystalline form.XRD spectra confirm the cubic structure of thin films having 221-Pm-3m space group.FESEM and EDX analysis exhibits uniform rod-like morphology with an estimated amount of elemental contents.The density of states spectra acquired through TB-mBJ approximation for electronic properties demonstrates the p-d hybridization in pure WO 3 and prominent f-orbital contribution in Gd containing compositions.The bandgap value was recorded as 1.73 eV using simulations and 2.27 eV with experimental for pure host material which tend to decrease with doping of Gd.Thermoelectric parameters corroborate an increase in charge carrier concentration by raising temperature and Gd-content.The see-beck coefficient exhibited a parabolic trend because of the effect of minority charge carriers.The refractive index was found to decrease while the static dielectric constant increased with the doping of Gd.The maximum values of refractive index and dielectric constant were observed as 3.04 and 7.89, respectively.The optical parameters present significant variation with doping and provide more reliable results for applications of these compositions in photovoltaics and optoelectronics.

Figure 7 (
Figure 7(d) presents the specific heat capacity of pure and Gd-doped WO 3 as a function of temperature.Pure WO 3 shows little rise in specific heat capacity but with Gd-doped WO 3 it shows comparatively much higher values of specific heat capacity.It is observed from the figure that the maximum value of specific heat capacity is obtained at maximum temperature values.Hence, the temperature rise revealed the increase in entropy and internal energy of the material.

Table 1 .
Crystallographic details of pure and Gd-doped WO 3 .

Table 2 .
Elemental compositions of pure and Gd-doped WO3 obtained through EDX.

Table 3 .
Comparison of this work and literature values of optical parameters of pure WO 3.