Optical properties and complex refractive index of Co-doped ZnO waveguide thin films elaborated by spray pyrolysis

CoxZn1-xO\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{Co}}_{x}{\text{Zn}}_{1-x}{\text{O}}$$\end{document} (x = 0.00, 0.04, 0.08, and 0.10) thin films were sprayed pyrolysis onto ordinary glass substrates. The micro-Raman spectroscopy revealed the presence of wurtzite structure in all films. The UV–Vis investigation showed good optical transmittance in the visible region with the increase in the absorption bands related to internal Co+2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{Co}}^{+2}$$\end{document}d–d transitions over Co concentration. The optical gap energy decreased by 0.34 eV as Co doping increased, contrary to Urbach energy which increased by 230 meV. The SEM observation indicated grain shape modification of the surface morphology of the films in addition to slight decrease in the grain size. M-lines spectroscopy measured the ordinary refractive index which was found to increase by 0.0156 as the Co doping increased. Cobalt doping provoked the extinction of light coupling and propagation in the films manifested as an increase in full width at the half maximum of the guided peaks and a decrease in the reflected intensity. This was due to the increase in the extinction coefficient measured by UV–Vis spectroscopy.


Introduction
The developments of all forms of optical waveguides led to huge development in numerous fields like integrated optics, lasers, and photonics. Optical fibers are relatively flexible and immune to electromagnetic interference so they found use in communications. Transparent thin films waveguides are of high quality, controllable, and efficient and by that, they had been employed as bio and chemical sensors [1][2][3], integrated optical amplifier [4], a guided layer in total internal reflection fluorescence microscope [5], and strain sensor [6] to name a few. A dielectric waveguide can be defined as any structure used to control the flow of electromagnetic waves in a certain direction. This guiding is possible by confining the electromagnetic wave within its surfaces. In order to understand the propagation of light in a waveguide, it is essential to characterize the refractive index and the extinction coefficient of the waveguide as the refractive index is a measure of the phase difference between the source wave and oscillating charges in the media and the extinction coefficient is a direct measure of the attenuation of the wave inside the media [7].
Dilute magnetic semiconductors (DMS) are materials that integrate new properties based on magnetic effects to a semiconductor host due to transition metals (TM) dopant such as V, Co, Cr, Mn, and Fe. DMS proved to be very unique devices in the microelectronics industry due to the fact that they exhibit spin-dependent magneto-electro-optical properties [8]. Therefore, a broad range of semiconductor devices can be conceptualized, including spinpolarized light-emitting diodes [9], spin-transistor logic devices [10], and lasers [11]. TM element doing offer control over both ferromagnetic and optical properties of wide gap semiconductors [12]. The incorporation of transition elements such as Co occupying substitutional sites give rise to crystal field splitting in the 3d levels of Co þ2 . These transition are manifested in optical measurements [13,14]. In addition, hybridization between the Co þ2 d level and ZnO electronic states resulting in the contribution of s Co þ2 to the conduction band minimum and d Co þ2 to valance band maximum. The spin dependency transport via the sp À d exchange interaction (coupling) between Co and ZnO constitutes the main characteristics of Co-doped ZnO DMS [15]. The CdMnTe DMS on GaAs substrate was demonstrated as successful waveguide to achieve integrated optics [16] opening new path of investigating and applying DMSs as waveguides.
In the last decade, Zinc oxide (ZnO) related researches grew largely because of new or improved types of electronic and photonic devices [17]. Waveguide structures based on ZnO have been demonstrated, suggesting that ZnO thin films bears a potential use in optoelectronics and integrated optics [18][19][20][21]. Co-doped ZnO DMS where elaborated and tested for several applications such as mono modal waveguide [22] and tunneling magnetoresistance device [23]. For a better understanding and control over ZnO thin film waveguide, it is necessary to perform an accurate and direct characterization of its optical properties especially the refractive index. For that, several techniques are used such as ellipsometry, which can reveal the refractive index, thickness, and extinction coefficient [24]. Prism coupler based method alternatively called m-lines spectroscopy has been developed since the '70s to characterize thin films. It measures the refractive index with 2 Â 10 À4 accuracy and the thickness with 0.5% [25].
The effect of dopants on the refractive index of ZnO is not very obvious and is still a subject of interest. The root of the optical properties of a semiconductor is intimately related to both intrinsic and extrinsic effects. Intrinsic ones are manifested via the transitions taking place between the electrons and holes in the conduction and in the valence band, respectively, in addition to excitonic effects due to the Coulomb interaction. Extrinsic properties are directly related to dopants, which usually create electronic states in the band gap, and hence influence both optical absorption and emission processes [17]. Control over the optical gap energy of ZnO was possible by variety of dopants [26][27][28]. The investigation concerning the application of DMS as waveguides are very scarce and prism coupler technique proves to be a very adequate tool for that.
This work investigates the complex refractive index, i.e., the refractive index and the extinction coefficient via the correlation between m-lines and UV-Vis spectroscopy of bi-modal Co-doped ZnO thin films elaborated by spray pyrolysis.

Experimental
The sprayed solution for the undoped ZnO  O] dissolved in methanol to produce the following contents of zinc and cobalt: Co x Zn 1Àx O with x equals 0.04, 0.08, and 0.10 ( Fig. 1).
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 spray pyrolysis at a deposition temperature of 450 C.
In order to characterize our thin films, multiple techniques were used. For the structural properties micro-Raman was employed (Horiba Jobin Yvon HR800) at excitation wavelength of 473 nm. Scanning Electron Microscope (SEM) JEOL JSM-7001F model for surface morphology. Finally for the optical measurements, Metricon 2010/M Prism coupler with rutile TiO 2 prism: n e = 2.8639 and n o = 2.5822 at 632.8 nm with an apical angle of 44.60 was used to couple 632.8 nm He-Ne laser light into air/Co x Zn 1Àx O/glass waveguide in addition to Shimadzu UV-3101PC UV-Vis-NIR Scanning Spectrophotometer with wavelength resolution of 1 nm.

Micro-Raman spectroscopy
Micro-Raman spectroscopy was used to study the impact of cobalt impurities on the crystal structure of ZnO thin films. This method permitted to detect disorder and defect due to dopant incorporation. Figure 2 showed the micro-Raman spectra of pure and Co-doped ZnO thin films in the range of 70-700 cm À1 . The ZnO has wurtzite structure so it possess 6mm (6 6v ) crystal symmetry. There are 4 atoms per unit cell which leads to 12 phonon, 9 of them are optical and 3 are acoustic. These phonons dispersion at the center of Brillouin's zone is written as: [29,30]. The undoped ZnO sample exhibited two clearly Raman-active peaks appeared around 102 and 441 cm À1 in addition to a very weak hump around 570 cm À1 . The peaks at 102 and 440 cm À1 were associated with E 2 (low) of nonpolar vibration for heavier Zn atom and E 2 (high) of oxygen displacement, respectively [29,31,32]. In fact, the weak hump was the result of two overlapped peaks localized at 537 and 577 cm À1 and were ascribed to A 1 (low)/E 1 (low) [33,34]. Co-doped ZnO thin films showed similar peaks of the undoped sample with decrease in intensity of the oxygen displacement peak (E 2 (high)) and the enhancement of the mixed A 1 (Low)/E 1 (low) peaks. In the work of Thongam et al. [35] about ZnO thin films, it had been reported that the mixed A 1 (Low)/E 1 (low) peaks were due to the crystal imperfection and defects such as zinc interstitials and oxygen vacancies. Also, Ponnusamy et al. [36] reported that these peaks arose possibly because of defects. In any case, the Raman behavior of our thin films can be ascribed to the substituted

UV-Vis measurements
The optical transmission spectra of undoped and Co-doped ZnO thin films in the range of 350-800 nm were depicted in Fig. 3. All films exhibited good optical transmittance. In the region ranging from 500 to 750 nm we can clearly observe a decrease in the average transmittance from 84 to 57 % with the increase of cobalt concentration. The observed spectra were very similar to those obtained in the literature for Co-doped ZnO thin films [37][38][39][40][41]. Due to the similar ionic radii of Zn þ2 (0.60 Å ) and Co þ2 (0.58 Å ) [13,42] the substitution of Zn þ2 by Co þ2 ions in the tetrahedral coordinated structure was apparent as absorption bands at 568, 613, and 658 nm. These bands were attributed to electronic transitions in 3d levels of Co þ2 (d-d transitions) [43][44][45]. Furthermore, the sharp absorption edge experienced a red shift upon Co doping indicating the decrease in the optical band gap. The optical band gap E g was calculated using the Tauc relation [46,47]: where a is the absorption coefficient, hm is the photon energy, B is a constant, and the exponent m depends on the nature of electronic transition (m = 1/2 for allowed direct transition of ZnO optical band). The optical band gap energy of all films was calculated by linear interpolation of ðahmÞ 2 versus hm (Fig. 3). The values decreased from 3.15 to 2.81 eV as Co doping increased from 0 to 10 at.% (Fig. 4) due to crystal field splitting of Co þ2 3d levels by the wurtzite structure. These new electronic states give rise to new donor electronic states just below the conduction band, in other words, the decrease in the optical band gap was the result of hybridization between Co þ2 and ZnO electronic states, mainly the contribution of s Co þ2 to the conduction band minimum of ZnO [14,[48][49][50][51][52]. The Urbach energy is a characteristic parameter of energetic disorder in the band edge. It was calculated based on the next equation [53]: where a 0 is a constant, hm is the photon energy and E U is the Urbach energy. Figure 4 depicted the evolution of the Urbach energy as a function of Co at.% dopant. It had been found to increase over Co content. This was a positive indication for the increase in the energetic disorder present in the films which is directly related to structural defects. This was in good correlation with the increase in the intensity of A 1 (low)/E 1 (low) peaks as a function of Co doping according to Raman spectra.  [54] for sprayed pyrolysis Co-doped ZnO thin films. In any case, the homogeneity across large-scale makes our thin films suitable for waveguiding applications.

M-lines measurements
In order to understand the effect of Co doping on the waveguiding properties of ZnO thin films, we used prism coupler technique to measure the thickness and the ordinary refractive index in the Transverse Electric (TE) polarization. The dispersion curves for the TE polarization is given by the following equation: where n, n a and n s are the refraction indices of the film, superstrate, substrate, respectively. m is the mode number. n eff is the effective index of the mode m and k 0 ¼ 2p k is the wavevector in vacuum. For at least two propagation modes (m ¼ 0 and m ¼ 1) [55], we can calculate the refractive index and the thickness by simultaneously solving the resulting equations [56,46].
For a plane wave traveling inside a lossy media in the form of a slob waveguide in the z direction, where a is the absorption coefficient, b is the phase constant and they are given by: where k is the extinction coefficient. The extinction coefficient k was evaluated using UV-Vis measurement as it is directly related to the absorption coefficient and can be calculated using the transmittance T and the thickness d of the films as indicated by the following relation [58]: The effective index was evaluated by m-lines spectroscopy using the Snell-Decartes equation of refraction [59]: where n p , n a and h p are the refractive index of the prism, the superstrate, and the base angle of the prism, respectively. By varying the incident angle on the prism's side h, we can excite many modes. Figure 6 presented the reflected intensity vs. the angle of incidence in the TE polarization. All films experienced two guiding modes. The curves exhibited extinction behavior with Co doping through the diminishing intensity and broadening of the peaks indicating the degradation of the light coupling and propagation in the films.
In order to explain the behavior of the refractive index with the optical band gap evolution, we adopted the single-oscillator approximation [60,61]. The refractive index is expressed in term of the energy of the incoming light E by the following expression: where E d is a measure of the strength of inter-band optical transitions, E o is the single-oscillator energy. According to Wemple-DiDomenico model, the single-oscillator energy can be approximated in terms of the optical gap energy as: E g % E o 2 . The value of E d for Zn þ2 is close to that of Co þ2 [62] and it was supposed to be unchanged.
The ordinary refractive index, the extinction coefficient, and the Full Width at Half Maxima (FWHM) of the m-lines peaks were plotted in Fig. 7. The ordinary refractive index experienced a slight increase upon cobalt content. In fact, the introduction of Co into ZnO had a decreasing effect on the optical gap which increased the refractive index according to the previous equation of the single-oscillator approximation. The decrease in the optical gap energy lowered the energy for electrons to be able to oscillate and contribute to the phase difference measured as an increase in the refractive index [7,63]. In other words, the electronic polarizability which originates from the electronic cloud deformation was facilitated by the decrease in the optical gap energy. The extinction coefficient had a similar behavior. The introduction of Co in the films rendered the films to be more absorbent at 632.8 nm due to Co þ2 d-d transitions in the visible region as previously discussed in the UV-Vis section. The propagation of the coupled light was less efficient as the attenuation of light increased with Co dopant in the thin films. This effect was confirmed by the width broadening and diminishing in intensity of m-lines peaks with their angular position remained virtually the same [25,64]. Fig. 6 The reflected intensity of the TE polarization for two guided modes as a function of the incidence angle for undoped and Co-doped ZnO thin films

Conclusion
In this work we had reported the successful deposition of Co-doped ZnO thin films by spray pyrolysis. All films had a wurtzite structure according to micro-Raman spectroscopy. A decrease in the intensity of oxygen displacement peak (E 2 (high)) and an increase in intensity of structural defects peaks (A 1 (Low)/ E 1 (low)) were observed over Co doping . According to UV-Vis measurements, the introduction of Co in ZnO had also induced the creation of new intrinsic and extrinsic electronic states. Optical band gap was found to decrease with Co doping due to electronic states hybridization between Co þ2 and ZnO. The energetical defects evolution had been confirmed by the Urbach energy calculation. M-lines spectroscopy allowed for the measurements of the ordinary refractive index and it increased as the Co doping increased which was attributed to the decrease in the gap energy based on the single-oscillator approximation. Furthermore, ZnO thin films developed absorbing behavior with Co which was obvious in the increase in both the full width at half maximum of the guiding peaks and the extinction coefficient in addition to the decrease in the reflected intensity. This was related to internal d-d transitions which affected light coupling and propagation. The correlation between m-lines and UV-Vis measurements seems to be very reliable method to measure the complex refractive index of relatively high refractive index transparent waveguide. It is simple and inexpensive in comparison to other optical techniques. This paper acts as a guidance in optimization of Codoped ZnO as a wave guide since the introduction of Co in the films promotes magnetic effects in ZnO yet the same dopent deteriorates its waveguiding properties. Therefore an optimal Co dopent percentage must be considered when designing Co-doped ZnO DMS waveguide.

Author contributions
YB conceived the idea of the articles and m-lines measurements. The elaboration of the films in addition to UV-Vis and micro-Raman measurements were carried out by HD scanning electron microscope images were performed by IS. All others contributed to the interpretation of the results and provided critical feedback and helped shape the research, analysis, and manuscript.

Funding
The authors have not disclosed any funding.

Data availability
The datasets generated during and/or analyzed during the current study are included in the manuscript and available from the corresponding author on reasonable request.

Declarations
Conflict of interest There are no conflicts of interest between the authors.