Optical and dielectric properties of electrochemically deposited p-Cu₂O films

Figure 1(a) shows the linear sweep voltammetry (LSV) curve of FTO substrate in a solution containing 0.2 M copper (II) sulfate and 3 M lactic acid with scan rate of 20 mV s⁻¹, pH and temperature of the bath were maintained at values 9 and 60 °C respectively. The potential range is between −1.3 and 0 V versus SCE. It is clearly shown in the figure that there are two reduction regions. We were interested in the first region that was detected between −0.23 V and −0.6 V in which there is the deposition of cuprous oxide Cu₂O according to the following mechanism [21]:

$$\begin{eqnarray}&&{{\rm{Cu}}}^{2+}+{e}^{-}\leftrightarrow {{\rm{Cu}}}^{+}\end{eqnarray} \tag{ 1 }$$

$$\begin{eqnarray}&&2{{\rm{Cu}}}^{+}+2{{\rm{OH}}}^{-}\leftrightarrow {{\rm{Cu}}}_{{\rm{2}}}{\rm{O}}+{{\rm{H}}}_{{\rm{2}}}{\rm{O}}\end{eqnarray} \tag{ 2 }$$

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Cu₂O films were synthesized at the selected potential of −0.5 V. Figure 1(b) represents the shape of current transient of Cu₂O thin films. The shape of the curve indicates clearly the nucleation-growth step [21], the curve exhibits three regions, the first region corresponding to the double-layer charging at the interface of FTO/electrolyte, in which the current density increases until the maximum current (I_max) is reached at a maximum time t_max. The second region corresponds to the nucleation and growth of Cu₂O nuclei, in this step the cathodic current density decreases due to Cu₂O film cover the surface. Finally, the cathodic current density value become steady with increase deposition time due to growth process of the Cu₂O film on the FTO substrate.

Figure 2 shows the XRD pattern of Cu₂O thin films electrodeposited on the conductive substrate FTO at different time 15, 30 and 60 min, respectively. The several peaks shown by the XRD pattern confirm polycrystalline nature of Cu₂O thin film which has cubic structure according the JCPDS N°: 05-0667 [22]. Moreover, the XRD patterns show obviously no secondary phases. The films deposited at 15, 30 and 60 min are oriented preferentially along [111] direction with lattice parameter a = 4.26 Å. When the deposition time is varied from 15 to 60 min, a clear increase of (111) peak intensity is observed indicating an improvement in the crystallinity of the films.

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The crystallite size of the samples deposited was estimated by using Scherrer formula (equation (3)) [23].

$$\begin{eqnarray}&&D=\displaystyle \frac{0.9\lambda }{\beta \,\cos \,\theta }\end{eqnarray} \tag{ 3 }$$

Where D, k, λ, θ and β are the crystallite size, a constant equal to 0.9, the wavelength of the x-ray, the diffraction angle and the full width at half maximum (FWHM) of the diffraction peak, respectively.

The dislocation density (δ), defined as the length of dislocation lines per unit volume, was evaluated from the formula (equation (4)) [24]:

$$\begin{eqnarray}&&\delta =\displaystyle \frac{1}{{D}^{2}}\end{eqnarray} \tag{ 4 }$$

Strain (ε) of the films was calculated by the formula (equation (5)) [24]:

$$\begin{eqnarray}&&\varepsilon =\displaystyle \frac{\beta \,\cos \,\theta }{4}\end{eqnarray} \tag{ 5 }$$

The calculated values of the lattice parameter, the crystallite size, the dislocation density and the microstrain are summarized in table 1. The calculated crystallite size is increased from 62.83 nm to 66.53 nm when the deposition time is varied from 15 to 60 min. While, the δ and ε decrease from 2.533 × 10⁻¹⁴ to 2.259 × 10⁻¹⁴ lines m⁻² and 0.551 × 10⁻³ to 0.52 × 10⁻³, when increasing the deposition time from 15 to 60 min. This is due to a decrease in defect levels and grain boundaries as well as an increase in crystallite size [25].

The SEM micrographs with two magnifications of each Cu₂O thin films prepared at different deposition times of 15, 30 and 60 min are presented in the figures 3(a)–(c) respectively. The all micrographs clearly show that samples have a homogeneous distribution of high nanometric grains cover uniformly the surfaces, dense microstructures and void-free surface. In each sample, the grains are well defined, hierarchical shapes and inhomogeneously sized. It is worth noting that when deposition time increases, from 15 to 60 min, a noticeable increase in grain size is observed. In fact, the average grain size for the samples of 15, 30 and 60 min are 520, 670 and 850 nm respectively.

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The Mott-Schottky analysis was used to characterize the electrodeposited Cu₂O films with different deposition time. The sign of Mott-Schottky plots identify the conductivity type of the deposited Cu₂O films. A positive slope of the linear part of the curve presents n-type conductivity, while a negative slope indicates p-type conductivity [26]. The linear region of Mott-Schottky plots for the deposited Cu₂O films at different time are shown in figure 4. All Cu₂O films deposited at 15, 30 and 60 min exhibit negative slopes as shown in figure 4, indicating p-type conductivity. The origin of p-type conductivity of Cu₂O films has basically been agreed on the formation of Cu vacancies [27, 28]. Mott-Schottky measurements used also to estimate the flat band potential (V_fb) and the carrier density, the equation is presented as [26]:

$$\begin{eqnarray}&&\displaystyle \frac{1}{{C}^{2}}=\displaystyle \frac{2}{{N}_{A}e\varepsilon {\varepsilon }_{0}}\left(V-{V}_{fb}-\displaystyle \frac{KT}{e}\right)\end{eqnarray} \tag{ 6 }$$

Where C, e, ε₀, ε, N_A, V_fb, V, T and k are the space-charge capacitance, the electron charge, the permittivity of free space, the relative permittivity, the carrier density, the flat band potential, the applied potential, the absolute temperature and the Boltzmann constant, respectively. The obtained carrier densities and the flat band potentials of the Cu₂O films from the Mott-Schottky measurements are listed in table 2. The flat band potentials of the p-type Cu₂O films increased from 0.438 V to 0.458 V with increasing of deposition time. The acceptor densities of the samples decrease with improvement of crystallinity. These results of carrier concentrations for Cu₂O thin films are in good agreement with those reported in the literature [18, 29].

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Optical absorption studies are important to determine the optical band gap of semiconductor films, and for understanding the optoelectronic properties of our growing semiconductor. The absorbance spectra in the visible region of the deposited Cu₂O thin films synthetized at different deposition times are displayed in figure 5(a). We observe from the showed spectra an absorption edge localized between 500 and 600 nm which corresponds to the excitonic band gap of Cu₂O. Moreover, figure 5(b) illustrates that the sample electrochemically grown at 15 min exhibits a higher transmittance. We observe that the transmittance was significantly decreases with increasing of deposition time. The plots of (αhν)² versus (hν) obtained from optical transmittance spectra for all samples is shown in figure 5(c). From the straight lines of plots of (αhν)² versus (hν), we conclude that the deposited films have a direct forbidden band gaps. Using the linear extrapolation method, the values of band gap energy of Cu₂O films deposited at 15, 30 and 60 min are estimated to be 2.32, 2.22 and 2.17 eV, respectively. Our finding results are in good agreement with literature data for Cu₂O films prepared by both chemical and physical deposition approaches [22, 30, 31].

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The absorption coefficient α of Cu₂O thin films was evaluated from the transmittance data using relation (equation (7)), where α, T and d are the absorption coefficient, the transmittance and the thickness of Cu₂O films, respectively [32].

$$\begin{eqnarray}&&\alpha =\displaystyle \frac{1}{d}\,\mathrm{ln}\left(\displaystyle \frac{1}{T}\right)\end{eqnarray} \tag{ 7 }$$

Figure 5(d) shows that the absorption coefficient increases with increasing growth time and showing a maximum value around 10⁴ cm⁻¹ in the visible range 2.4–3 eV. We conclude that when the deposition time increases, an enhancement in the absorption coefficient of Cu₂O thin films is observed. The absorption coefficient is used to define the Urbach parameter (E_u) corresponding to the transitions between the extended states of the valence band and the localized states of the conduction band. The absorption coefficient is related to Urbach parameter by the following formula [33]:

$$\begin{eqnarray}&&\alpha ={\alpha }_{0}\exp \left({\rm{h}}\nu /{{\rm{E}}}_{{\rm{u}}}\right)\end{eqnarray} \tag{ 8 }$$

$$\begin{eqnarray}&&\mathrm{ln}\,\alpha =\,\mathrm{ln}\,{\alpha }_{0}+\left(\displaystyle \frac{h\nu }{{E}_{u}}\right)\end{eqnarray} \tag{ 9 }$$

The Urbach energy E_u is determined by plotting lnα versus photon energy (hυ) as shown in figure 6. The results are summarized in table 3, the Urbach energy decreases with increase of deposition time. E_g optical band gap values change inversely with E_u energy. The results of Urbach energy are comparable to those reported by authors interpreting it as the bandwidth of the states located within the band gap width.

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The more critical optical constant of a semiconductor material is refractive index, its relationship with wavelength of incident light is known as dispersion name [34]. The refractive index is expressed as n = n* + ik, where n* is the complex refractive index, and k is imaginary refractive index also named as extinction coefficient as it indicates the total optical loss caused by transmittance and scattering. The n and k can be calculated from the following relations [34]:

$$\begin{eqnarray}&&n=\displaystyle \frac{1+R}{1-R}+\sqrt{\displaystyle \frac{4R}{{(1-R)}^{2}}-{K}^{2}}\end{eqnarray} \tag{ 10 }$$

$$\begin{eqnarray}&&K=\displaystyle \frac{\lambda \alpha }{4\pi }\end{eqnarray} \tag{ 11 }$$

where the parameters α, R and k are absorption coefficient, reflectance and extinction coefficient. Figures 7(a), (b) shows the refractive index (n) and the extinction coefficient (k) as a function of wavelength of the Cu₂O films synthetized with different deposition times. We conclude that with increasing of wavelength, the refractive index and extinction coefficient values decrease, this is attributed to normal semiconducting dispersion behavior of the material. In other hand the extinction coefficients and refractive index values are influenced by the deposition time, and both increase with it. The slight increase can be attributed to an increase in density of the films with increasing deposition time. Table 4 shows the values of 'n' and 'k' on wavelength 1100 nm for all films. The found values are similar with the literature [35–37].

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In semiconductors the fundamental electronic transition is allied to the wavelength dependent complex dielectric constant, expressed as: ε_r + iε_i. The real (ε_r) and imaginary parts (ε_i) of complex dielectric constant can be calculated from the extinction coefficient and refractive index using the following equations [38]:

$$\begin{eqnarray}&&{\varepsilon }_{r}={n}^{2}-{k}^{2}\end{eqnarray} \tag{ 12 }$$

$$\begin{eqnarray}&&{\varepsilon }_{i}=2nk\end{eqnarray} \tag{ 13 }$$

The variation of real and imaginary dielectric constants as a function of the wavelength for thin films deposited at different time are presents in figures 7(c) and (d). It is observed that real and imaginary parts follow the same pattern, in the other hand the real values are higher than the imaginary values and both their values increases slightly with deposition time.

The optical conductivity allows to study conveniently the optical response. The optical conductivity (σ_opt) has been determined from the relation [38]:

$$\begin{eqnarray}&&{\sigma }_{opt}=\displaystyle \frac{\alpha nc}{4\pi }\end{eqnarray} \tag{ 14 }$$

where α, n and c are the absorption coefficient, the refractive index and the velocity of light, respectively. The plots of optical conductivity (σ_opt) as a function of photon energy for Cu₂O films are shown in figure 8. We conclude that optical conductivity increases with increase of photon energy (hv) and deposition time. The increasing of σ_opt can be attributed to the increase of absorption coefficient (α) and refractive index (n). The increase in photon energy improves the movement of electrons, so the optical conductivity reaches the highest values. The values of 'ε_r', 'ε_i' and 'σ_opt' for different deposition time are calculated at the wavelength 1100 nm and listed in table 4.

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