1. Introduction

Zinc oxide is a direct, wide band gap semiconductor material with many promising properties for blue/UV optoelectronics, transparent electronics, spintronic devices, antireflection coatings, transparent electrodes in solar cells and gas sensor applications^[1-6]. ZnO has been commonly used in its polycrystalline form for over a hundred years in a wide range of applications: facial powders, ointments, sunscreens, catalysts, lubricant additives, paint pigmentation, piezoelectric transducers, varistors, and as transparent conducting electrodes, thin film^[7-10]. Its research interest has waxed and waned as new prospective applications revive interest in the material, but the applications have been limited by the technology available at the time.

ZnO has numerous attractive characteristics for electronics and optoelectronics devices. It has a direct bandgap energy of 3.37 eV, which makes it transparent in visible light and operates in the UV to blue wavelengths a high exciton binding energy of 60 meV^{[1, 2]}. This material can be deposited by various methods like reactive evaporation, molecular beam epitaxy (MBE)^[11], magnetron sputtering technique^[12], pulsed laser deposition (PLD)^[13], the sol–gel technique, chemical vapor deposition, electrochemical deposition^[14] and spray pyrolysis^[15], have been reported to prepare thin films of ZnO. Among these, we will focus more particularly in this paper on the spray ultrasonic technique that is a low method suitable for large-scale production, it has several advantages in producing nanocrystalline thin films, such as a relatively homogeneous composition, a simple deposition on glass substrate because of the low substrate temperatures involved, easy control of film thickness and fine and porous microstructure. It is possible to alter the mechanical, electrical, optical and magnetic properties of ZnO nanostructures^{[9, 10]}.

The aim of this paper is study the possibility of the correlation between the optical and electrical properties of ZnO thin films with precursor molarity. Recently Ivill et al.^[16] established the inverse correlation between the magnetization of Mn doped film with carrier density. They identified the Mn oxide precipitation even at $x=$ 0.03 in the doped films prepared at very high oxygen pressure (20 mTorr), and controlled the resistivity from 195 to 0.185 $\Omega$$\cdot$cm by introducing Sn (0–1 at.%) as a co-dopant. Vollmann el al.^[17] studied the relations between the morphology and conductivity of thin films; and they have concluded that the conductivity depends primarily on the compactness of the film morphology and the crystallite length and secondarily on the orientation of the crystallites. Therefore Asadov et al.^[18] described the correlation between structural and electrical properties of ZnO thin films as a good agreement between the experimental data obtained by XRD, SEM and conductivity measurement.

In this paper, ZnO thin films were deposited on a glass substrate at various precursor molarity between 0.05 to 0.125 mpl/l-1 at a substrate temperature of 350 ℃ , the films were deposited by a spray ultrasonic technique. We have studied the effect of the spraying concentration on electrical conductivity and optical properties, and also study the possibility to estimate a correlation between the electrical conductivity and the optical band gap with the precursor molarity.

2. Experimental and methods

2.1 Experimental procedure

The spray solutions were prepared by dissolving (Zn(CH$_{3}$COO)$_{2}$, 2H$_{2}$O) in the solvent containing equal volumes absolute ethanol solution (99.995%) purity, then added a drop of HCl solution as a stabilizer, the mixture solution was stirred at 50 ℃ for 180 min to yield a clear and transparent solution. The samples were deposited, keeping the substrate temperature $T_{\rm S}$ equal to 350 ℃ , and with the precursor solution concentrations $M$ of 0.05, 0.075, 0.1 and 0.125 mol/L. The substrate cooling was prevented by spraying a solution jet of 2 min pulses with each new pulse delayed by 10 min from the previous one. The film forms as the solutions atomized aerosol droplets vaporize on the heated substrate. This procedure has led to highly adherent ZnO films. The distance between the substrates and the spray gun nozzle was fixed at 3.5 cm^{[19, 20]}.

The optical properties of the deposited films was measured in the range of 300–800 nm using an ultraviolet–visible spectrophotometer (UV, Lambda 35) and the electrical conductivity of the films was measured in a coplanar structure obtained with evaporation of four golden stripes on the film surface. All spectra were measured at room temperature (RT).

2.2 Methods and model

The aim was to study the correlation between the electrical and optical properties of undoped ZnO thin films with the precursor molarity. The reported relationships between the band gap and the lattice parameters ($a$ and $c$) showed very large variations from linearity descript by Ton-That et al.^[21] and plotted the band gap as a function of lattice constants $a$ and $c$. However, the same works investigated the dependence of the physical properties of ZnO thin film as a function of parameter conditions such as temperature, thickness, oxidizing conditions, nitrogen addition and doping for characterizing the thin films^[22-29].

The correlation between the electrical and optical properties were studied for the electrical conductivity ($\sigma )$ as a function the band gap energy ($E_{\rm g})$ and precursor molarity $M$ of ZnO films. These parameters were resulting from the following equation:

$\begin{cases} \sigma _{(\ast )} =\dfrac{\sigma _{\rm (e)} }{\sigma _{\rm (e)Max}}, \\ E_{\rm g(\ast )} =\dfrac{E_{\rm g(e)} }{E_{\rm g(e)Max}}, \\ M_{(\ast )} =\dfrac{M_{\rm (e)} }{M_{\rm (e)Max}}, \\ \end{cases}$

(1)

where $\sigma _{\rm (e)}$, $E_{\rm g(e)}$ and $M_{\rm (e)}$ are the experimental values; $\sigma _{\rm (e)Max}$, $E_{\rm g(e)Max}$ and $M_{\rm (e)Max}$ are maximal experimental values and $\sigma _{(\ast )}$, $E_{\rm g(\ast)}$ and $M_{(\ast )}$ are the first values that have been consisted in the correlate relationships.

3. Results and discussion

3.1 Electrical conductivity

Figure 1 shows the variation of the electrical conductivity $\sigma$ of ZnO films as a function of precursor molarity. As can be seen, the electrical conductivity increases from 0.24 to 7.96 ($\Omega$$\cdot$cm)$^{-1}$ with the increasing of precursor molarity of ZnO thin films, which means an increase in the carrier concentration. The increase in the conductivity of films with increasing precursor molarity has been explained by the decreasing of the Urbach energy (fewer defects) (Table 1) in the films hence the potential barriers decreased and defects decreased, which resulted in an increased carrier density^[30-32].

3.2 Optical properties

Figure 2 shows the absorbance spectra of ZnO samples obtained at different precursor molarities. It is clear that, the absorbance at photon energy smaller than 3.1 eV is low. This indication is confirmed with the absorbance value and the tail height of ZnO films were obtained by increasing the precursor molarity and reached a minimum at 0.1 M, followed by an increase with the precursor molarity further increasing. We note that the concentration of the spray effect is clearly observed in the layer quality. From Fig. 2, it can be seen that the extrapolation of the linear portion of the graph to the energy axis at $A$ $=$ 0 gives an optical band gap energy $E_{\rm g}$ as shown in Table 1^{[33, 34]}.

ZnO is a semiconductor with a large direct band gap; the optical gap energy $E_{\rm g}$ (Table 1) was obtained from the transmission spectra using the following relations^{[34, 35]}:

$A=\alpha d=-\ln T,$

(2)

$(Ah\nu )^2=C(h\nu -E_{\rm g}), \quad A=\alpha d,$

(3)

where $A$ is the absorbance, $d$ is the film thickness; $T$ is the transmittance spectra of thin films; $\alpha$ is the absorption coefficient values; $C$ is a constant, $h\nu$ is the photon energy and $E_{\rm g}$ is the energy band gap of the semiconductor, as is shown in Fig. 3. The typical variation of $(Ah\nu )^2$ as a function of photon energy ($h\nu )$, is determined by extrapolation of the linear region to $(Ah\nu )^2$ $=$ 0^[36]. It can be observed that Figure 4 indicates a large blue shift of the band gap corresponding to the absorption edge in the layers due to the transition between the valence band and the conduction band. Moreover, we have used the Urbach energy, which is related to the disorder in the film network, expressed as^[37]:

$A=A_0 \exp \frac{h\nu }{E_{\rm u}},$

(4)

where $A_0$ is a constant and $E_{\rm u}$ is the Urbach energy, as shown in Table 1.

Figure 3 shows the variation of the band gap energy $E_{\rm g}$ and the Urbach energy $E_{\rm u}$ as a function of the spray concentration. We have obtained an increase of the optical gap energy for the films deposited at spray concentrations between 0.05 to 0.1 M, which may be attributed to the similar ionic radius between O and Zn^[38], the band gap energy is broader due to the increase in the transition tail width, which the increase of carrier concentration and blue shift effect, as reported in the literatures^[39]. We found that the optical gap energy and transparency are affected by spray concentration. The decrease in the Urbach energy (Fig. 3) is attributed to the decrease of the defects as expressed in the literatures^{[40, 41]}.

3.3 Correlation between the electrical and optical properties

We have previously described the experimental data; one can see from this data that the electrical conductivity of the ZnO thin film is varied nonlinearly to the precursor molarity. The model proposed for the ZnO thin film with precursor molarity is discussed.

We have estimated the relationships between the electrical conductivity and the band gap energy and the precursor molarity in all films. We found the following empirical relationships:

$\sigma _{\rm (c)} =a b^{E_{\rm g(\ast )} } M_{(\ast )} ^c,$

(5)

where $\sigma _{\rm (c)}$ is the correlated electrical conductivity; $a$, $b$ and $c$ are empirical constants as $a\approx$ 0.0003105, $b\approx$ 5697 and $c\approx$ 2.761. The results are collected in Table 2.

The variation experimental electrical conductivity and correlation of ZnO thin films as a function of optical and gap precursor molarity is shown in Figs. 4 and 5, respectively. One can see that this correlation indicates that the measurement in the electrical conductivity of the films from the optical band gap and the precursor molarity was equal; it is predominantly influenced by the transition tail width of undoped ZnO thin films.

In our experience there was no evidence for significant changes in electrical conductivity with correlation upon varying the band gap energy; the main effects have been observed upon variation of modifying the precursor molarity. This difference could be caused by the different compositions. The correlation between the electrical conductivity and the band gap with the precursor molarity was investigated.

4. Conclusion

In summary, high-quality transparent ZnO thin films were deposited on glass substrates by the ultrasonic spray technique. The description of correlation between electrical conductivity and optical gap energy with precursor molarity were discussed. The ZnO films exhibit higher electrical n-type semiconductors, in which band gap energy increased from 3.08 to 3.37 eV with an increasing of precursor molarity of 0.05 to 0.1 M. The maximum value of electrical conductivity of the films is 7.96 ($\Omega$$\cdot$cm)$^{-1}$ obtained in ZnO thin film for precursor molarity of 0.125 M. The correlation between the electrical and the optical properties with the precursor molarity suggests that the electrical conductivity of the films is predominantly influenced by the band gap energy and the precursor molarity. The measurement of the electrical conductivity of the films with correlation it is equal to the experimental with the error is about 1% in the higher conductivity.