Effect of Cu incorporation on optoelectronic properties of e-beam evaporated ZnO thin films by Ellipsometric investigations

Electron beam deposition technique has been used to deposit a series of Zn 1-x Cu x O nanocrystalline thin film on silica substrate with a variety of Cu concentrations. The microstructural, surface morphology and spectroscopic ellipsometry (SE) were used to examine the physical properties of the deposited films. The nanocrystalline nature of the Zn 1-x Cu x O (0.0≤x≤0.20) thin film has been confirmed by surface morphology studies. The XRD spectrum of the Zn 1-x Cu x O nanocrystalline film showed a hexagonal wurtzite type structure, and no extra phase was detected. Our results show that as the Cu content increases, the direct optical energy gap E g decreases without any sign of solubility limit up to x≤0.2. The decrease in E g can be attributed to the sp-d exchange coupling. In addition, exploring the spectral behavior of the refractive index dispersion from SE of the Cu-doped ZnO shows that as the Cu dopant increments; the refractive index of the deposited film enhances. Further, understand the refractive index dispersion of the deposited film has been performed using a single oscillator model proposed by Wemple-DiDomenico (WDD). Our calculations show that as the Cu concentration increases, the values of oscillator energy E o decreases however, the dispersion energy E d increases. As a result, the variation of the optical energy band gap and the tunability of the dispersive oscillator parameters values E o , E d , n 0 ,  0 , M -1 and M -3 with the increase of the Cu doping level confirm that Cu doped ZnO films are a good candidate for optoelectronic device applications.


1-Introduction
Zinc oxide (ZnO) is still a promising semiconductor, because it has a high exciton binding energy of 60 meV at room temperature, direct wide band gap of 3.37 eV [1], chemically stable, good transparency in the visible wavelength, high electronic conduction, good luminescence at room-temperature, cheap, and low toxicity matter. As a result of these fascinating properties, ZnO is very suitable for use in many applications, such as optoelectronic devices [2], photocatalysis [3], solar cells [4], UV fabric protectors [5] and gas sensing devices [6]. Many workers have already fabricated ZnO films using various techniques, including spray pyrolysis [7], reactive magnetron sputtering [8,9], chemical vapor deposition (CVD) [10], sol-gel [11] molecular beam epitaxy [12], and pulsed laser deposition [13,14]. Recently, a lot of researchers increase the potential of using ZnO by doping it with transition metals like Fe, Mn, Co, Ni and Cu [15]. Among the family of transition metals, Cu is very important metal for doping due to its high electrical conductivity and almost similar ionic radii as that of ZnO. Literature studies show that Cu doping into ZnO matrix can enhance its various physical, chemical and optical properties [16]. Commonly, doping causes the appearance of new acceptor levels and electron donors in the band structure of the doped material. These levels appear in the gap, between the conduction band and the valence band [17,18]. The theoretical investigation shows that Cu doping can reduce band gap of ZnO leading to shift of the luminescence [19]. For copper doping, studies have shown that 5%-10% Cu-doped ZnO has a lower band gap value than undoped ZnO [20,21]. The crystallite size of the film increased as the doping ratio of Cu increased from 2 wt % to 10 wt %.
Increase in Cu doping leads to an insignificant decrease in the optical band gap of the thin films [22] and the nanoparticles were within the 32-38 nm range and the Cu dopant uniformly substituted Zn positions [23]. Other results show that Cu doping did not lead to the formation of a secondary phase, but slightly reduced the particle size [24] and the valence state of Cu in ZnO was confirmed to be +2. It was found that the impurity level of 0.1% copper element is above the Fermi level, indicating that Cu-doped ZnO is a p-type semiconductor [25].
The manuscript is summarized as follows:  Part 2 describes the physical method used to produce and characterize nanocrystalline Zn1-xCuxO(0.0≤x≤0.2) in powder and thin film forms.

Materials and Methods
Cu doped ZnO ingots with different Cu concentrations (0, 4,8,12,16, and 20 at.%) have been synthesized using mechanical mailing method. Analytical grades with stoichiometric ZnO and CuO powders (with a chemical purity of (99.999%, Aldrich) were mixed together and milled in a mechanical ball mill machine at 200 rpm for 6 hours. The mixture is made into disk-shaped to avoid splashing the mixture powders during the evaporation process. The prepared pure and Cu doped ZnO ingots were used as a source for thin film deposition. The ZnO and Cu doped ZnO thin films with various Cu concentrations were deposited by electron beam evaporation technique (Edward Auto 306) at room temperature. Amorphous glass with a size of (25mm×25mm) is used as the substrate. To clean the substrate carefully, the substrate was immersed in acetone for 15 minutes, and then washed with purified water for 15 minutes, and subsequently with alcohol for 10 minutes. At last, the substrate was ultrasonically cleaned in deionised water for 15 minutes, and then was dried in air at a temperature of 100°C. The substrates and ingots have been placed in the chamber, which was then evacuated at pressure of 5 ×10 -6 Pa. The pellet ingot was preheated for 5 minutes before evaporation to remove any pollutants and degas the pellets. The distance from the substrate to the source is kept at about 20 cm. The thickness of the film was adjusted at 300 nm at a deposition rate of 2nm/sec, which was controlled by a thickness monitor device (model; FTM6). More details of the deposition methodology are explained elsewhere [26,27,28,29,30,31,32].

Characterization techniques
X-ray diffractometer (XRD, Cu-Kα = 1.54056Å, Philips diffraction 1710) was used for crystallographic investigation. The ratio of the elemental composition of the film was checked by using energy dispersive X-ray spectroscopy (EDXS). The surface morphology of the film was performed using an atomic force microscope (AFM, model MLCT-MT-A). The vertical resolution of the AFM device is about 0.2 nm. The AFM cantilever is provided by NANO-WORLD, its cross-section is 4.5x4.6 μm 2 , the length is 160 μm, and it works at a resonant frequency of 285 kHz. Both sides of the cantilever are plated with platinum-iridium of about ~ 23 nm, and the tip is sharp with radius nearly less than 10nm. Non-contact mode is used to obtain the AFM image of the film surface. Optimized scan parameters is adjusted to supply the finest picture resolution whereas maintaining the speed and size of scan at 5 ms/pixel and 1x1 µm 2 , respectively. The optical properties of nanostructured Zn1-xCuxO (0.0≤x≤0.2) film were studied using variable-angle reflection SE instrument. SE apparatus has a revolving optical compensator and is also operational with a programmed retarder. The SE spectra is measured in the angular range 60 o -75° with 5 o steps [33,34,35].

Elemental composition analysis
The elemental composition analysis of Cu-doped ZnO films with different Cu doping levels has been performed by EDXS measurement.    It is worth noting that, the XRD spectra did not show any foreign peak related to copper phases such as copper oxide and or copper cluster, indicating a successful inclusion of Cu 2+

Structural and microstructure characterizations
ions into the ZnO lattice without change of the structure of ZnO. It was found from Fig. 2(b) that the peak position of (002) plane is shifted towards lower diffraction angles (34.48-34.42 degree) due to the Strain introduced in the film by the partial replacement of Cu +2 ions by Zn +2 in the ZnO structure of semiconductor matrix with remarkable expansion in the cell volume. 79-0205. This behavior was given in literature for ZnO doped Mn [37] and ZnO doped Cu thin films [38]. In addition, the nanostructure nature of the films is examined by using Debye-Scherrer's equations from the calculations of the mean crystallite sizes, and lattice microstrain,    [39]. As shown in Figure 5, the introducing of Cu ions into the ZnO matrix will cause the grain size to decrease, which is correlated to the inhibition of the nucleation growth mechanism (bad crystallinity), leading to lattice distortion [40], thereby degradation of crystallinity. This means that there is tensile micro strain embedded in the ZnO lattice. These practical observations are in accordance with the reported results of Mndoped SnO2 [41], Ni-doped SnO2 [42], Mn doped ZnO [43].

Surface morphology analysis
The microscopic description of the surface morphology of the undoped and Cu doped ZnO films has been performed using AFM investigation. research [44,45]. Furthermore, it was found that the surface roughness and RMS surface roughness are decreased from 4.01 nm to 3.4 nm and from 3.8 nm to 3.2 nm, respectively with the increase of the Cu concentration from 0 at.% to 20 at.%. The reduction in the surface roughness with the increase of Cu doping into ZnO films [38] and CuTe films [46] is reported in literature. It has to be mentioning that the grain size obtained from AFM is higher than the crystallite size calculated by XRD. This inconsistency can be ascribed to the fact that the crystallite size is a record of the size coherent scattering domain, whilst the grain size is a set of this coherently scattering domain separated by grain boundary. Besides, crystallite size reveals two distinct ranges when dislocations are located in the composition, while the difference between them is not visible in the AFM micrographs [42].

Spectroscopic ellipsometric investigation of nanostructured
The terms rp and rs shown in relation 1 are the Fresnel coefficients of light waves polarized parallel to and vertical to the plane of incidence, respectively, and Δ is difference in phase between the parallel and the vertical component of the polarized wave. Spectra of ψExp .and ΔExp. of the Zn1-xCuxO film with different Cu contents measured when the incident angle is equal to 70° is depicted in Fig 7(a,b). In the 600-1100 nm spectral range, the ψExp. spectra show obvious oscillations. This oscillation occurs due to the overlapping between light waves reflected from the top surface and the light waves go during the film. The spectral oscillation observed in the ψExp. spectrum indicates that the film under investigation is transparent. Near to the energy band gap of the studied film (250-590nm), the oscillation disappears, indicating that the absorption process has begun. A theoretical optical model was proposed in order to extract the physical properties of the studied film (surface irregularities, optical parameters (n & k) and film thickness) from the ψExp. and ΔExp. spectra, see Fig. 7(a, b). Regarding the physical properties, the proposed model must match the actual structure of the studied film.
Using the proposed optimization simulation program of the optical model of fitting parameters that matches the actual sample structure, the n and k of the studied film can Fig.7 (a,b). For different Cu concentration (x = 0.0, 0.04, 0.08, 0.12, 0.16, 0.2) ZnO film, the spectral characteristics of the SE parameters Ψ and Δ with wavelength is measured at the incident angle θ=70 o be obtained from the matching of the experimental and simulated SE spectra of ψExp., ΔExp., ψCal. and ΔCal., respectively. By reducing the mean square error function (MSE) calculated using Levenberg-Marquardt mathematical relation, the equivalent between the measured SE parameters ψExp., ΔExp. and the calculated SE parameters ψCal., ΔCal. can be obtained. The mathematical relation of Levenberg-Marquardtis [44,45,50]: ). Soon, we reached a good agreement between the calculated results of the proposed optical model and the measured SE parameters ψExp. and ΔExp., so that the wavelength dependence of the optical constants of the studied film can be determined. In the following paragraphs, we will give more detailed discussion of the optical model developed for SE data analysis of Zn1-xCuxO thin films [51, 52 53].

Optical Model
The response of the film to the externally incident polarized photon field can be fully explained by its complex dielectric relation (ε(E)=ε1+iε2) from which the optical behavior of the thin film material can be obtained. Building an appropriate optical model and using nonlinear fitting procedure, microstructure parameters such as film surface irregularity, thickness and nonuniformity of film thickness can be extracted from ψExp. and ΔExp. The 9-10, nice coincident between the measured SE parameters (ψExp., ΔExp.) and the calculated SE parameters (ψcal., Δcal.) in the entire recorded wavelength regime is achieved. The MSE values generated by the harmony between measured and calculation SE parameters are 1.12 and 1.11 for ZnO and Zn0.84Co0.16O, respectively. In addition, the fitting activity also produce approximate value for the thickness of the film and surface irregularity which are 214±0.44nm, 3.90nm, 211±0.41nm and 3.60nm for ZnO and Zn0.84Co0.16O, respectively. As we have noticed, the surface irregularity extracted from the SE fitting scheme is in very good coincidence with the value obtained from the AFM measurement reported earlier in the morphology investigation section.

Absorption process occurs in nanocrystalline Zn1-xCuxOthin film
This section is much concerned with the optical properties of nanocrystalline Zn1-xCuxO films extracted from the previously developed optical model. First, the absorption occurs in the Zn1-xCuxO nanocrystalline film is considered, and, the spectral dependence of the refractive index of the Zn1-xCuxO nanocrystalline film is examined later. The complex permittivity ( ) of the Zn1-xCuxO nanocrystalline film is obtained as a direct consequence of the coincidence between measured SE factors (ψExp., ΔExp.) and the calculated SE factors (ψcal., Δcal.). The optical factors (n & k) of the studied films are correlated to the value of ε1(λ) and ε2(λ) through the mathematical formula: The wavelength dependence of the absorption coefficient α(λ) occurring inside nanocrystalline Zn1-xCuxO film is linked directly to the extension coefficient k(λ) via the formula:  As shown in Figure 11, the spectral dependence of the parameter k(λ) of nanocrystalline Zn1-xCuxO films with different Cr contents is calculated through the relationship k(λ) = α(λ)λ/4π.
The results presented in Fig.11 show that at shorter wavelength below 350 nm the value of k rises with increasing of Cu dopant. Since the energy of the propagated photons is quite close to the energy band gap of the investigated Zn1-xCuxO film, this behavior can be expected.
Once we have the dispersion of the extinction coefficient k(λ) then we can easily calculate the parameter α (E). Figure 12 illustrates the dependence of the absorption coefficient α (E) of the Zn1-xCuxO film with different Cu doping on the photon energy. Obviously, the onset of absorption processes close to and above the energy gap Eg≈2.7eV-4.2eV is clearly observed, therefore, as expected the absorption coefficient α(E) rises up with the increment of the Cu level. In contrast, the absorption coefficient becomes almost flat (region of transparency) below 1.5eV up to 2.6eV. The apparent rapid decline of the absorption curve with decreasing photon energy is basically attributed to the absorption, in which electrons transition through the energy gap to reach conduction band of the studied film. Using the well-known Tauc relationship, the optical energy gap Eg can be extracted using the following relationship [58]: In the previous equation (Eq.8), the parameter n refers to the index indicating the type of optical transition process and αo is constant. When n = 1/2 the optical transition referred to the allowed direct energy inter-band. According to Eq.8, Eg is derived by identifying the intersection of the linear portion of the extrapolation of (αhν) 2 with respect to (hν) at (αhν) 2 = 0. The direct band gap of the Zn1-xCuxO (0.0≤x≤0.2) nanocrystalline film has been calculated based on the (αhν) 2 vs. (hν) diagram. Fig. 13 indicates that as the Cu concentration increases  [60,61]. In contrast, the bottom part of the conduction band (CB) of ZnO is built from 4s of Zn with strong contributions of Zn 3d, O 2s and O 2p states observed at higher energies [60]. As mentioned earlier, the interaction of different energy states of Zn and O atoms results in the formation of wurtzite ZnO of hexagonal crystal structure [61]. When the Cu +2 atom is introduced into ZnO matrix, it will replace the cation site Zn +2 of the ZnO structure. Since both Zn and Cu atoms own d-electrons, therefore, the intra-atomic interaction for the intensely related d-electrons will form so called d-d interactions. The partial replacement of Zn +2 by Cu +2 leads to the existence of d-state of Cu +2 , which is energetically close to the Zn +2 d in VB of the ZnO matrix. The d-d interaction between Cu +2 and Zn +2 will result in the formation of a hybrid state close to the valence band of the ZnO crystal, which consequently will reduce the energy gap of ZnO [62]. Our results show that as the doping level of Cu in ZnO semiconductor matrix (Zn1-xCuxO (0.0≤x≤0.2)) increases from 0 % to 20 %, the energy gap reduces from 3.29 eV to 2.93 eV. Fig.13. For nanocrystalline Zn1-xCuxO films with different Cu contents the variation of (αhν) 2 as a function of photon energy (hν) is depicted.

Refractive Index characteristics of Zn1-xCuxO thin film
The refractive index of a thin film is one of the essential properties because it level. The reason is that the refractive index of a substance is directly related to its polarizability through the Lorenz-Lorenz equation [63], where the polarizability of a material increases with the increase of the atomic radius of the atoms that make up the material.
Therefore, replacing Cu with a larger atomic radius (1.38Å) with Zn with a smaller atomic radius (1.28Å) can increase the polarizability and consequently increasing the refractive index. This behavior is clearly manifested in Fig.15 in wide spectral range. This manner of n is very consistent with the reported results of Ni and Cr doped SnO2 synthesized by spray pyrolysis deposition technique [42,64], respectively. In Fig. 15, solid lines of different colors represent the fitted lines of the experimentally extracted refractive index dispersion of Cu doped ZnO. The mathematical formula explaining the fitted line is the two terms Sellmeier dispersion relation, and its form is: In Eq.9, two constants A and B are employed as fitting parameters.

Optical characteristic of dispersive oscillator parameters
By applying the Wemple and DiDomencio (WDD) single oscillator model, it is possible to have a deeper understanding of the spectral behavior of the refractive index and the dispersion energy parameter. The mathematical relationship describing the WDD model is [65,66]: In relation 10, the factors n, Ed, Eo and E = hν are index of refraction, dispersion energy, average oscillator energy and energy of the incident photon, respectively. These factors are related directly to the internal structure of the studied film, among them, Ed which is related to electronic oscillator strength and Eo is related to oscillator energy, and consequently to the average energy band gap of the investigated film. By analyzing the energy dependence of the factors (n 2 −1) −1 verses (E 2 ) for nanocrystalline Zn1-xCuxO (0.0≤x≤0.2) film below the edge of the band gap using WDD model. Rewriting Eq.10, the normal dispersion of the nanocrystalline Zn1-xCuxO (0.0≤x≤0.20) film will have the form: Using straight line fitting technique to Eq.11, the calculated values of Eo and Ed factors are estimated from the graphical representation of (n 2 −1) −1 and (hν) 2 given in Fig. 16. Table 1 lists the WDD oscillator factors calculated for nanocrystalline Zn1-xCuxO (0.0≤x≤0.20).  [53]. Obviously, WDD approximate optical band gap ( ) opt WDD g E is consistent with the values determined from Tauc's graph [67]. Besides, the physical interpretation of WDD formula reveals a strong relationship between Ed and the chemical structural changes of the deposited nanocrystalline Zn1-xCuxO (0.0≤x≤0.20) film (such as lattice structure, chemical bonds, etc.) [Error! Bookmark not defined.]. Therefore, as the Cu content increases, the increase in Ed is associated to the increase in the observed lattice parameters, see Fig. 3. Additionally, Table 1 not only contains WDD oscillator parameters Eo, Ed but also the corresponding static refractive index n0=(1+Ed/Eo) 0.5 (n when E → 0) and static dielectric constant

Conclusions
Nanocrystalline Cu-doped ZnO thin films with various Cu concentrations were prepared using e-beam deposition technique. The physical properties of the nanocrystalline Cu-doped ZnO films were studied by using different characterization methods such as XRD, EDXS, AFM and SE. The XRD spectrum of Zn1-xCuxO (0.0≤x≤0.1) nanocrystalline film shows the formation of a hexagonal wurtzite type structure without any additional phases.
The morphology analysis shows that the grain size and the surface roughness decrease with increasing of the Cu doping level which is confirmed from XRD and SE investigations, respectively. It was found that the direct energy gap of the Zn1-xCuxO (0.0≤x≤0.2) nanocrystalline film decreases with the increase of Cu content. The direct optical energy band gap reduction of the studied film is ascribed to the sp-d exchange interaction. The refractive index dispersion shows that as the Cu doping level raises, the refractive index enhances. The