Optoelectronic and birefringence properties of weakly Mg-doped ZnO thin films prepared by spray pyrolysis

MgxZn1−xO thin films were deposited on glass substrate with x varied between 0.01 and 0.05 by spray pyrolysis at a temperature of 450 °C. The structural investigation showed that all thin films had ZnO wurtzite structure with a preferred (002) orientation. The gap energy was calculated using Tauc’s plot, and it decreased over the Mg content by 0.07 eV. The charge carriers’ density dropped by an order of 105 as Mg content increased whereas the resistivity and the mobility increased. SEM observations revealed a significant difference between undoped and doped thin films. A 632.8 nm laser source prism coupler revealed 2 optical modes for every thin film in each Transverse Electric and Transverse Magnetic mode, and the birefringence of the Mg-doped films was positive. Both ordinary and extraordinary refractive indices were found to decrease as the Mg content increased. Great intention has been paid to the relation between the refractive, charge carriers’ density, and the optical band gap.

To modify its electrical properties, ZnO was doped with Group III elements such as Al, Ga and In which acted as donor dopants to reinforce its n-type electrical nature and group V elements such as N, P, As, and Sb which acted as acceptor dopants which changed ZnO to be a p-type semiconductor [23]. Controlling the refractive index of ZnO thin films was achieved by several ways including thermal annealing [24] and doping with In [25], Te, N [26], and Mg [27]. However, the effect of dopants on the optical and electrical properties of ZnO is still not well understood.
Tailoring ZnO optical and electrical properties via dopants while maintaining high-quality films especially using spray pyrolysis is very attractive to both scientists and technology developers as it offers a control over several experimental parameters, it is cheap, uncomplicated, and environmentally friendly.
wurtzite Mg x Zn 1-x O alloy is very interesting due to the high solubility of Mg in the ZnO wurtzite matrix (up to 30%) [28]. Moreover, it offers control over a range of optical and electrical properties of ZnO such as widening of the optical gap energy up to 0.85 eV [29]; consequently, it can be used for multiple purposes such as a top layer in Mg x Zn 1-x O/ZnO multilayer UV photodetector [30] and high-mobility MgZnO/ZnO thin-film transistor [31] to name few. Concerning the waveguiding properties, little attention has been paid to wurtzite Mg x Zn 1-x O as a waveguide; however, Mg x Zn 1-x O was used as a buffer layer for ZnO waveguide thin film [32]. In another work, a potential use of Mg x Zn 1-x O cubic rocksalt-type phase as a wave guide was reported by Yu et al. [33]. wurtzite Mg x Zn 1-x O thin-film alloy refractive index was previously studied, but there is still work to be done, as there are opposite results regarding the birefringence which was found to be negative in some studies [21,34] and positive in another study [27].
In this work, we engaged in the investigation of the relations between the refractive index, the optical gap energy, and the charge carriers' density in addition to the birefringence of Mg x Zn 1-x O thin films deposited by spray pyrolysis on glass substrate.

Experimental
The sprayed solution for the undoped ZnO thin films was prepared by dissolving the proper amount of dihydrate zinc acetate [Zn(CH 3  Ordinary glass substrates were ultra-sonically cleaned in a 1:1 mixture of acetone and ethanol for 15 min and left to dry in air. The films were deposited using HALLMARK pneumatic spray pyrolysis system in the following conditions: the nozzle-substrate distance was 15 cm, the atomizing carrying gas was air at pressure of 2 bar and the flow rate was kept at 1 mL/min. The deposition temperature was 450°C. In order to characterize our thin films, multiple techniques were used: Philips PANalytical X'Pert Pro diffractometer with a wave length of 1.5406 Å , scanning electron microscope JEOL JSM-7001F model, and for the electrical properties, Ecopia HMS-3000 hall effect measurement system, finally for the optical measurements, Metricon 2010/M Prism (rutile TiO 2 : n e =28639 and n o =2.5822 at 6328 nm with an apical angle of 44.60°). Coupler was used to couple 632.8 nm HeNe laser light into air/Mg x Zn 1-x O/glass waveguide, Shimadzu UV-3101PC UV-Vis-NIR Scanning Spectrophotometer with wavelength range of 190-1100 nm and resolution length range of 0.1 nm in addition to FL3-DFX-iHR320 photoluminescence at room temperature.
(JCPDS card no. 00-036-1451) with the quasi-predominance of (002) peak indicating the preferential growth of undoped and Mg-doped ZnO thin films through the c-axis direction. However, weak intensity peaks of other crystallographic directions were observed in the following positions 31.96°(100), 36.56°(101), 47.87°(102), 63.17°(103) and 72.85°(004). The peak (002) experienced a shift towards higher angles over Mg doping (Fig. 1b) which was reported by a number of authors [35][36][37], and it is due to the difference in the ionic radius between Mg ?2 (0.57 Å ) and Zn ?2 (0.60 Å ) [38]. This difference was directly related to the compression strain on the main axes of the wurtzite structure a and c. Previously, Chang et al. [39] also reported similar compression strain in their sputtered MgZnO thin films which were interpreted by good substitution between Mg and Zn ions.
The grain size can be calculated by the Debye-Scherrer formula [35]: where k is the wavelength of the incident X-ray, h is the Bragg angle, K is the shape factor (0.9 for Gaussian fit), and b is the Full Width at Half Maxima (FWHM) of the peaks. The crystallite size, lattice parameters, and strain axes are tabulated in Table 1.

UV-Vis measurements
As Fig. 2 depicts, the transmittance of the thin films was slightly enhanced on average with the introduction of Mg in the visible region (400-800 nm). The limit of the absorption zone was shifted to smaller wavelengths which renders the thin films to be more dielectric as Mg doping was increased, this effect is directly related to the blue shift of the optical band gap, and it was approximated for each film using the Tauc equation and plotted in Fig. 3: where hm is the photon energy, E g is the optical gap energy, A is constant, and n equals 1/2 since ZnO has a direct band gap. The widening of the optical band gap could be ascribed to the difference in electronegativity between Zn ?2 and Mg ?2 ions [40][41][42]. In similar study, Al-Ghamdi [43] reported this correlation between the optical band-gap energy and the electronegativity in his work about amorphous Se 96-x Te 4 Ag x thin films. In fact, it should be noted that both the electronegativity and electron affinity are directly related [44]. In this way, Fig. 4 presents the calculated optical band gap and the electron affinity versus Mg doping. The electron affinity (ev) was quantitatively calculated using Vegard's law [45]: where ev(ZnO) and ev(MgO) have the values of 4.5 eV [46] and 0.85 eV [47] for the electron affinity of ZnO and MgO, respectively. Previously, Iskenderoglu et al. [28] experimentally approved UPS technique of the inverse relation between the optical gap energy and the electron affinity of sprayed MgZnO alloy thin film, with Mg doping ranging from 0 to 15%.

Photoluminescence
The room-temperature photoluminescence spectra are shown in Figure 5.  Figure 6 demonstrates the near isotropic electric transportation of the deposited films which could be Mg Concentration (at. %) attributed to the fact that the films have the predominant orientation (002) of the wurtzite structure [52]. From Fig. 7, the free charge carriers' density decreased from 3.146 9 10 18 for the undoped film to 9.273 9 10 13 cm -3 for Mg 0.05 Zn 0.95 O film. In parallel, the resistivity increased from 109 to 1268 X cm, and the mobility increased from 0.01821 to 53.08 cm 2 / (V.s). The decrease in charge carriers' density could be attributed to the fact that the conduction band (CB) of pure ZnO consists mainly of O 2p and Zn 4s states [53,54], so the introduction of Mg in ZnO thin films will reduce the Zn 4s state and introduce Mg 3p state which has high energy relative to the Zn 4s [55,56]. Moreover, the widening in the optical banggap energy discussed previously, could also influence the free charge carriers' density since the electrons passing from the valance band must require higher energy to access the conduction band. Figure 8 shows the morphology of undoped and 5 at.% doped ZnO thin films. At first sight, the brightness of undoped film was higher than that of the doped one, this was in agreement with the enhancement of the dielectrical behavior with Mg doping. The undoped (left image) thin film showed a dense surface with granular mixture of small grains and large aggregates. The size of the small grains varies from * 20 to 80 nm and that of the aggregates reached * 200-300 nm. From the doped sample (right image), it was evident that magnesium had a tendency to promote the phenomenon of coalescence. This doped film showed a less dense and relatively homogeneous morphology with large aggregates of which size varied from * 200 to 500 nm. The increase in pores and nonhomogeneous size distribution in 0.1 at.% and 0.3 at.% Mg-doped ZnO thin films relative to undoped one prepared by sol-gel on Si (100) substrate was reported by Hussain et al. [40] which is in alignment with our results; however we should mentioned that contrary results also were reported by Hashim et al. [57] concerning the enhancement of surface density and the diminution of pores in 0.05 M:Mg-doped ZnO thin film. Due to the complexity of the phenomena governing thin films formation, it is not intuitive to conclude the general effects that Mg doping has on ZnO films surface morphology. Neither cracks nor empty holes were observed on the surface of the films, revealing the high quality of our films. In any cases, these surface morphologies seem to be suitable for waveguiding applications.

M-lines measurements
The M-lines measurements demonstrated the guiding modes present in the films. All films had four guiding modes (TE 0 , TE 1 , TM 0 , and TM 1 ) two for each optical polarization [Transverse Electric mode (TE) and Transverse Magnetic mode (TM)] as illustrated in Fig. 9.  Using the dispersion equations for TE and TM polarizations, the optogeometric parameters can be calculated [58,59]. The effective indices, the films thicknesses, and the birefringence values are presented in Table 2. Figure 10 illustrates the variation of n TE , n TM , optical gap energy, and free charge carriers' density as a function of the Mg concentration. The slight difference between n TM and n TE confirmed the birefringence behavior of our films. This made the guided waves traveling during the TE mode in the plane perpendicular to the c-axis of the wurtzite structure submit to an ordinary refractive index (n TE ) and during the TM mode to an extraordinary one (n TM ) [22]. Both n TE and n TM were found to decrease over Mg doping. This behavior seemed to be in good agreement with the broadening of the optical band gap and the depletion of the conduction band-free charge carriers' (Fig. 10) [60]. The birefringence was measured to be positive for all films which was a good indication of the insignificant change of the bond polarizability of Zn-O with the replacement of Zn by Mg [61,62].
The inverse relation between the optical gap energy, the resistivity, and the refractive index as Mg content increased in the ZnO thin film was also observed by Kaushal et al. [63]. The same fact had been reported by Teng et al. [27] for Mg-doped ZnO thin films prepared by pulsed laser deposition. In similar study, Sorar et al. [64] found that the ordinary refractive index generally decreased with the increase of the Si doping in ZnO thin films prepared by sol-  gel and annealed at 350°C and 550°C, whereas their optical band-gap energy was found to be blue shifted.

Conclusion
Mg-doped ZnO thin films were successfully deposited on glass substrate via spray pyrolysis at 450°C. The XRD characterization showed highly c-oriented thin films with a decrease in a and c as the Mg concentration increased in the thin films. The undoped thin film had a multisize grain distribution, meanwhile the Mg 0.05 Zn 0.95 O had a more homogeneous grain distribution. Mg doping in the ZnO films led to a blue shift of the optical band-gap energy and a depletion of the conduction band due to the drop in free carriers' density that had a direct effect on the ordinary and the extraordinary refractive indices that were found to decrease. The birefringence of a crystal depends on multiple factors such as strain, defects charge carriers' density, bounds orientations, and so on; therefore, it will change from papers to papers with the change of deposition method especially.

Author contributions
The first author contributed to the conception of the study. Films preparation was carried by OR, SS, and AM. AB acted as a guide through out the study. The m-lines measurement was done by YB; the hall effect and UV-Vis measurements were taken by the same; others were responsible for the films preparation. XRD was preformed by BR and AT. LB and HS performed the SEM measurements, and finally, MB was responsible for the photoluminescence. The first draft was written by the corresponding author and revised in correspondence with mainly the first author and the rest of the others in a lesser degree. Charge carriers' density Ln(n) Fig. 10 Ordinary (n TE ) and extraordinary (n TM ) refractive indices, optical gap energy, and charge carriers' density as a function of Mg concentration