Applying the Density Function Theory (DFT) combined with LCAO basis set and employing the B3LYP hybrid functional, the optimized geometrical parameters, electronic properties, as well as the Infrared and Raman spectra for wurtzite-ZnO structure were investigated.
Prior to computing, ZnO thin film prepared by the spray pyrolysis method is characterized by X-ray diffraction using Rietveld refinement. This analysis shows that ZnO has hexagonal wurtzite structure (
P6
3
mc) with lattice parameters,
a = 3.2467 and
c = 5.2151
Å in good agreement with our predicted optimized geometry. Atomic force microscopy (AFM), Raman spectroscopy and UV-Vis-NIR spectrophotometry techniques are used to explore morphological, optical and vibrational properties of the sprayed ZnO thin film. The computed band gap
is in excellent agreement with that deduced from UV-Vis transmission . The simulated infrared and Raman spectra were also calculated, anda good agreement with the measured spectra is obtained. Finally, a detailed interpretation of the infrared and Raman spectra is reported.
DFT Thin Film Electronic Structure IR and Raman Spectroscopy1. Introduction
Zinc oxide (ZnO) continues to garner an extensive research interest owing to several of its promising applications. It has been the object of the renewed research for a wide range of applications such as light emitting diodes [1] , laser diodes, gas sensor [2] , thin film solar cells [3] and spintronics [4]. The interest of ZnO resides especially in its wide direct band gap (3.4 eV), high n-type conductivity, high thermal conductivity and its large exciton binding (60 meV) [5]. Nevertheless, during the design, the control of structural defects as well as surface and interfacial structures is essential for optimizing the device performance [6]. In addition, it is noted that the growth conditions affect the band gap which is a key parameter in the design of optoelectronic devices.
Synthesis of ZnO thin films has been performed by several techniques, such as spray pyrolysis, sol-gel [7] , pulsed laser deposition [8] RF magnetron sputtering [9] and Chemical Vapour Deposition [10]. The spray pyrolysis technique has been selected owing to its large deposition area, low cost process, and viable approach of producing good quality films. Thus, a lot of work have been carried out and various parameters of the deposition of ZnO films such as, substrate temperature, carrier gas flow rate, solution flow rate, nozzle to substrate distance and film thickness have been optimized [11] [12] [13] [14] [15].
Several studies have been done on the electronic structure of ZnO in the wurtzite phase using abinitio calculations [16] [17] [18] [19]. Due to the various functionals employed, the theoretical band gap values cover a wide spectrum. Franklin et al. reported that physical origin of the changes in the band gap may be related to the trial basis set which is utilized for iterative solutions of the Kohn-Sham equations [20]. Also, Arrigo et al. showed that the severe underestimation of the band gap, which is mainly due to a wrong energy position of the d-bands of the Zn atoms, leads to an inadequate description of vibrational and dielectric properties [21]. Bernasconi et al. showed that optical response properties, computed with the Coupled-Perturbed-Hartree-Fock/Kohn-Sham method with hybrid functionals, can reach an accuracy comparable to experimental estimates for various classes of semiconductors and oxides [22]. Moreover, IR and Raman spectroscopy can offer valuable information on structural changes, lattice defects, grain size, and the concentration of impurities presents in the ZnO host lattice [23] - [28]. Cheng et al. have reported that the lattice dynamics in ZnO is very sensitive to the compositional disorder which introduces changes in the electronic properties and vibrational phonons [29]. Indeed, in the wurtzite structure of ZnO, the E2 phonon frequency can be affected by compressive stress, tensile stress, grain size, thickness of the film and mismatch of thermal expansion coefficients of the layer and the glass substrate [8]. Also, David et al. also reported that the E2 Raman active phonon is systematically affected by the particle size [30].
As far as we know, there is not yet in the literature IR and Raman spectroscopy using quantum mechanical calculations of the ZnO have been reported in detail. In the present work, first principle DFT calculations using B3LYP hybrid functional have been performed to investigate structural and electronic properties as well as infrared and Raman spectra of wurtzite structured ZnO. Specifically, we report a combined experimental and theoretical analysis of sprayed ZnO thin film. We discuss below the features of calculation method for simulating the structural parameters, electronic band structure, Infrared (IR) and Raman spectra that show a good agreement with our experimental data.
2. Films Preparation and Characterization Techniques
Zinc oxide thin films have been prepared on heated glass substrates at 460˚C by the spray pyrolysis technique. The starting solution is made up of Zinc acetate dihydrate (Zn(CH3COOH)2, 2H2O) (Sigma Aldrich, St. Louis, MS, USA, 99.0%) 0.01 M dissolved in a mixture of water and propanol with fraction volumes of 1/4 and 3/4 respectively and it was acidified with acetic acid (pH = 5) according to the experimental protocol described previously [10] [11]. Phase identification and structural analysis of the as-grown films, were carried out at room temperature by X-ray diffraction (Analytical X Pert PROMP D) with Cu-Kα radiation (λ = 1.54056 Å), at 40 kV, 100 mA. Data for the Rietveld refinement were collected in the 2θ range 30˚ - 65˚ with a step size of 0.017˚. The surface morphology was carried out by atomic force microscopy at taping mode (AFM, VEECO digital instrument 3A). The optical measurements of ZnO thin film were performed at room temperature using a Schimadzu UV 3100 double-beam spectrophotometer in the wavelength range 300 nm - 1800 nm. The micro-Raman spectra were recorded at room temperature with a Horiba Jobin HR 800 system. A 632.8 nm line of a He-Ne laser was used for off-resonance excitation.
3. Computational Method
First-principles calculations based on Density Functional Theory (DFT) using exchange-correlation (EXC) proposed by Frisch and coauthors in 1994 were performed which described by the following equation:
E X C B 3 L Y P = E X L D A + 0.20 ( E X H F − E X L D A ) + 0.72 ( E X G G A − E X L D A ) + 0.81 ( E C G G A − E C L D A ) + E C L D A (1)
Such hybrid functional employ the Becke functional allied to the Lee-Yang-Parr (LYP) adjustment to DFT and the Slater exchange plus Vosko, Wilk, Nusair (SVWN) to improve the formalism proposed by LYP. This calculation level was implemented in the CRYSTAL14 program package [31] [32].
An all-electron basis set of Gaussian-type functions which represent crystalline orbitals as a linear combination of Bloch functions has been adopted for oxygen and zinc. For oxygen, a [4s3p] basis as in [33] , together with an extra d (exponent 0.5) was employed, resulting in a [4s3p1d] basis set. For Zn, a [6s5p2d] basis set as in [34] was used. The geometries were optimized on the basis of the convergence of analytical gradients and nuclear displacements [35]. The diagonalization was performed using a grid of k points according to the Monkhorst-Pack method [36] and the shrinking factor was set to 8 × 8 × 8 corresponding to 50 independent k points in the Brillouin zone. Harmonic phonon frequencies at the center of the first Brillouin zone (Γ point) are obtained from the diagonalization of the mass-weighted Hessian matrix W of the second energy derivatives with respect to atomic displacements:
W a i , b j = H a i , b j M a M b (2)
where atoms a and b (with atomic masses Ma and Mb) in the reference cell, 0, are displaced along the i−th and j−th Cartesian directions, respectively. The relative intensities of vibrationnal peaks were simulated through an analytical approach. This formalism is based on combining gradients of mono-electronic and bi-electronic integrals [37] [38] with a coupled perturbed Hartree-Fock/Kohn-Sham scheme [39] [40] for the response of the crystalline orbitals to a static electric field. The convergence threshold of the energy for the selfconsistent-field (SCF) procedure has been set to 10−8 hartree for structural optimizations and to 10−10 hartree for vibration frequency calculations [41] [42].
4. Results and Discussion4.1. Microstructural and Rietveld Analysis
The structure refinement was carried out by the Rietveld analysis of the X-ray powder diffraction data with the FULLPROF software [43]. Figure 1 illustrates the calculated diffraction profiles and XRD patterns of as-synthesized ZnO thin film. The recognized diffraction peaks are consistent with those of a wurtzite structure [11] [12]. It is seen that the intensity of (002) peaks was most higher than all others peaks indicating that the latter is preferentially c-axis oriented. The reliability of the calculated pattern during refinement was checked by the profile residual RP, the weighted profile residual Rwp and the goodness of fit χ2. Refinement may be accepted for the weighted profile residual Rwp < 10 and goodness of fit χ2 < 2 [44]. On the basis of refined crystallographic data, the lattice constants, structural parameters, atomic positions and other fitting parameters of the sample are computed and given in Table 1. The primitive unit cell of the wurtzite structure comprising O-Zn-O bonds and contained two oxygen atoms and two zinc atoms is shown in Figure 2. Moreover, the arrangement of the oxygen atoms is similar to that of the zinc atoms, in which each atom is located at the center of a tetrahedron. On the other hand, it is found that the obtained value of d-spacing (2.5796 Å) for ZnO film was lower than that of the d-spacing for ZnO powder, suggesting that the film grains are compressed [45]. In addition, a study of the surface morphology of ZnO thin film was carried out by AFM (Figure 3). The surface of ZnO thin film appears smooth and contains smaller clusters with columnar shape and the root mean square (rms) was found to be 31.59 nm. Charpentier et al. reported that the column growth during the deposition of ZnO on glass substrate can be explained by the coalescence of the islands which leads to the formation of polycrystalline films by columnar growth of grains perpendicularly to the substrate plane [46]. These strongly oriented grains and broadening in experimental peaks from X-ray diffraction may be due to strain along the c-axis and the crystallite size. Assuming homogeneous strains, the crystallite size D and strain ε can be respectively estimated from the following equation:
{ D = 0.9 λ β cos θ ε = β 4 tan θ (3)
where β is the peak’s FWHM and θ is the Bragg angle.
Refined structure parameters for ZnO thin film
Space groupe
P 63 mc
Unit cell parameters
a(Å) c(Å) V(Å3) c/a
3.2467 5.2151 47.61 1.6063
Bond-length
dZn-O (Å)
2.6021
Discrepancy Factor
Rwp (%) Rp (%) RF (%) χ2
2.65 2.78 3.89 1.07
Site
Wyckoff Position
x
y
z Biso (Å2)
Occ
Zn O
2b 2b
1/3 1/3
2/3 2/3
0 0.38224
0.06500 0.07300
0.5 0.5
The estimated value of crystallite size (D) and strain (ε) are respectively of the order of 37.41 nm and 6.5610−4. These values are close to that previously reported [11] [12].
4.2. Structure and Optimization
The optimized geometry of ZnO bulk is obtained with DFT, employing hybrid functional B3LYP as implemented in the software CRYSTAL14. The structure of pure wurtzite-ZnO unit cell is fully optimized. The computed structural parameters and those refined from our experimental data through Rietveld analysis are presented in Table 2. We note that the deviation from the experimental value is only about 1%, meaning that our calculation is reasonable. Also, the values are in good agreement with other reported theoretical values in the literature [47].
Comparison of lattice constants of ZnO thin film by Rietveld analysis obtained from XRD with geometrical optimization
Unit cell parameters (this work)
Rietveld-analysis geometrical optimization
a(Å) c(Å) V(Å3) c/a
3.2467 5.2151 47.61 1.6063
3.28223712 5.27346980 49.20 1.6066
Site Wyckoff Position
x
y
z
x
y
z
Zn O
2b 2b
1/3 1/3
2/3 2/3
0 0.33 0.38224
−0.33 0.33
0.0653 −0.33
0.31538
4.3. Electronic Structure and Optical Properties
Figure 4 shows the transmittance and reflectance spectra of the ZnO film, which revealed an optical transmittance of above 75% in the visible range. In the range, where the absorption is high, the absorption coefficient a may be derived using the following equation [48]:
{ R + T = e − α d α = 1 d ln ( 1 − R ) 2 T (4)
where d is the layer thickness.
The band gap of ZnO thin film was calculated using the Tauc model by extrapolating the linear portion of the plot ( α h ν ) 2 versus incident photon energy ( h ν ). The extrapolation of the intersection of the line with the ( h ν )-axis at 3.3 eV gives the value of the optical band gap (Figure 5). It is found that the optical absorption coefficient ( α h ν ) near the absorption edge varies exponentially with incident photon energy, which is a measure of the width of the band tails of the localized states [49] [50]. The Urbach energy which indicates the width of the band tails of the localized states has been calculated from the slope of local straight line portions in the plot of ln ( α ) versus ( h ν ) (inset Figure 5). The Urbach energy EU value is of the order of 67.39 meV. These tails in the forbidden band affect the band gap value and govern the conduction mechanism. The obtained values of Urbach energy and band gap energy have been close to the values of our previous works in the literature [11] [12]. In addition, the optical properties are related to the band structure and density of states. The band structures of ZnO are shown in Figure 6. As shown in Figure 6, the bottom of conduction band and the top of valence band are located at the Γ point in the Brillouin zone, indicating that the ZnO is a direct band gap semiconductor. The calculated band gap is 3.35 eV, which is close to the optical band gap estimated from the ultraviolet-visible transmittance and reflectance spectra of the ZnO films (3.3 eV). It seems that the B3LYP functional provides a reliable band gap for ZnO. Other theoretical calculations cover a wide spectrum varying from 0.23 eV to 4.23 eV, mostly disagree with experimental measurements [51] [52]. These
strong difference in calculation mainly due to the choice of the basis set describing the ground state [20]. It is found that the basis set which include the d orbitals is expected to be an optimal basis set. Defects induced by structural disorder may lead to the appearance of localized states in the band gap, called band tails which can affect the Fermi level and this latter may lead to further discrepancies between observed and computed band gaps [5] [53]. It should be noted that the discrepancy between the computed and observed band gaps is of the same order of magnitude as the Urbach energy. The simulated Density of states (DOS) of wurtzite ZnO is shown in Figure 7 for the energy range −10 eV to +10 eV. The DOS reveals that the valence band is mainly formed by Zn 3d states and O 2p states, whereas the conduction band is essentially occupied by Zn 4s states. A similar density of states has been obtained by Chuanhui et al., while the gap is smaller [51]. Moreover, Zhi et al. reported that the strong interaction between O 2p and Zn 3d bands my lead to the observed difference between calculated band gap and the experimental one [16]. The band gap provides information on the electronic structure of the compound for the possible application in optoelectronic devices. IR and Raman spectroscopy are useful for the interpretation of the structure and bonding strength, and can provide a detailed understanding. Serrano et al. indicated that the discrepancy between the calculated and measured phonon modes is primarily related to the underestimated band gap [54].
4.4. Phonon Properties
According to the group theory, wurtzite structured ZnO belongs to the space group P63mc with unit of four atoms in the unit cell. At the Γ-point of the Brillouin zone, group theory predicts the following irreducible representations of the lattice optical phonons:
Γ O p t = 1 A 1 + 2 B 1 + 1 E 1 + 2 E 2 (5)
where B1 modes are IR and Raman inactive and the two non-polar E2 modes are only Raman active. In addition, the polar A1 and E1 modes are IR and Raman active, and therefore they split into longitudinal and transverse optical phonons (LO and TO).
The experimental Raman spectra with the corresponding theoretically simulated one are shown in Figure 8. All the calculated frequencies and their assignments are presented in Table 3. The experimental Raman spectrum of the ZnO thin film recorded at room temperature exhibits two prominent peaks at 110 and 450 cm−1 assigned to E2 (high) and E2 (low) Raman active mode in the wurtzite crystal structure [55]. A similar result has been observed in ZnO bulk and thin film [56]. The two non-polar E2 (high) and E2 (low) modes are associated with the vibration of oxygen (O) atoms and zinc (Zn) sublattice, respectively [57]. Thus, the E2 low mode corresponds to the vibration of the heavy zinc sublattice, while the E2 (high) mode is associated with the vibration of the lighter oxygen sublattice. In addition, the strong E2 (high) mode is an indication on the good crystallinity [58]. The DFT predicted Raman spectrum of ZnO exhibits three main intense bands located at 100 cm−1, 380 cm−1 and 425 cm−1 assigned to E2 (high), A1 and E2 (low) modes, respectively. The very weak band at 403 cm−1 is assigned to E1 mode. From these data, we remark that the agreement with our experimental results is quite satisfactory for E2 high mode, whereas the experimental frequency of the E2 Low mode is slightly lower than the simulated one. This discrepancy may be caused by structural defects. In fact, Wrzesinski et al. reported that tensile stress in the wurtzite-structure affects the E2 phonon wavenumber [59]. Furthermore, the compressive strain in the films that caused the Raman peaks shift was consistent with that obtained from the XRD result [57]. The calculated IR active optical phonon modes of wurtzite ZnO shows two peaks at wavelengths in the range from 0 to 900 cm−1 (Figure 9). The most characteristic bands are at 380 and 403 cm−1. These peaks are attributed to TO phonons of A1 and E1 modes [60]. The most intense peak at 403 cm−1 is assigned to Zn-O stretching vibrations [61]. Moreover, E1(TO) and A1(TO) modes reflect the strength of the polar lattice bonds [62].
Detailed assignments of theoretically computed IR and Raman vibrations of ZnO
(cm−1) Sym. IR IR intensity
Raman Raman intensity
100.3970
E2
I
A
156.94
379.5879
A1
A 665.80
A
236.60
402.5345
E1
A 1267.93
A
32.08
425.8058
E2
I
A
1000.00
5. Conclusion
In summary, this work deals with the X-ray diffraction, UV-Vis spectrophotometry, IR and Raman spectral investigations of sprayed ZnO thin film supported by first principle abinitio DFT calculations using hybrid (B3LYP) as exchange and correlation functional. Band structure and DOS of bulk wurtzite ZnO have been calculated. ZnO thin film has hexagonal wurtzite structure with a smooth surface and a growth in a preferred orientation along the direction (002). The optimized structural parameters of wurtzite structure of ZnO were found to be close to the experimental data. Our calculated band gap of 3.35 eV is in excellent agreement with the measured value of 3.3 eV. The simulated Raman spectra of ZnO were also similar to experimental data. The above results show the ability of the DFT to accurately describe and predict the electronic and vibrational properties of semiconductors.
Conflicts of Interest
The authors declare no conflicts of interest regarding the publication of this paper.
Cite this paper
Ouni, B., Larbi, T. and Amlouk, M. (2022) Vibrational, Electronic and Structural Study of Sprayed ZnO Thin Film Based on the IR-Raman Spectra and DFT Calculations. Crystal Structure Theory and Applications, 11, 23-38. https://doi.org/10.4236/csta.2022.112002
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