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Introduction
In previous years, the investigation of new materials for photovoltaic applications was dependent and related to the experimental and modelling parameters of any properties. Nickel oxide was obtained to belong in the group of semiconductor materials and is one of the best materials at present because of its good properties [1].
Nickel oxide (NiO) is a semiconductor material with a nature of p-type, which belonged to the part of TCO family. This attribute of NiO has several potential applications, for example, it is used in the gas sensors due to its band gap energy in the range of 3.6−4.0 eV and for the organic solar cells applications due to its p-type semiconducting [2]. It can be used in transparent diodes and even in the transparent transistors caused by the best optical transmission and electrical conductivity. Moreover, NiO can be used for defrosting windows due to its good conductivity, and fabricated NiO can be used in the UV photodetectors and touch screens due to its good responsivity [3, 4].
In the present article, we have studied and investigated a relationship to calculate the crystallite size (G) from the measured structural parameters of the X-ray diffraction in the NiO thin films. We have used the experimental data of NiO thin films prepared at several deposition temperatures in the range of 380–460°C [5], which present the following parameters, such as the diffraction angle 2θ, the full width at half-maximum (FWHM), the crystallite size G, the lattice parameter a and a − a0 of (111) diffraction peak for NiO thin films at several deposition temperatures.
Materials and Methods
The NiO samples were fabricated on the glass substrates using a pneumatic spray technique with 0.1 M of the precursor molarity. The NiO thin films were deposited at several deposition temperatures in the range of 380–460°C [5] (see Table 1).
The diffraction angle 2θ, the full width at half-maximum (FWHM), the crystallite size G, the lattice parameter a and a − a0 of (111) diffraction peak for NiO thin films at several deposition temperatures [5].
Deposition temperature Ts (°C)
2θ (deg)
β (rad)
G (nm)
a (nm)
a − a0 (nm)
380
37.80
0.00766
19.13
0.4122281
0.00537184
400
37.67
0.00781
18.74
0.4135872
0.00401271
420
37.64
0.00868
16.88
0.4138530
0.00374695
440
37.60
0.00799
18.31
0.4143484
0.00325152
460
37.66
0.00707
20.72
0.4136507
0.00394921
Table 1 presents that the NiO thin films were nanocrystalline and had a cubic structure with (111) crystal plane at the higher intensity, which has preferential a-axis orientation along with (111) crystal plane.
The Miller indices (hkl) were obtained from the Bragg equation [6]:
n\lambda = 2{d_{hkl}}\,sin\,\theta
where n, λ, dhkl and θ are the integers called the order of diffraction, the wavelength longer of X-ray (λ = 1.5406 A°), the interplanar spacing and the diffraction angle, respectively.
The lattice parameter a of cubic structure for NiO thin films was determined in Eq. (1) and XRD patterns using the following formula [5]:
{d_{h\,k\,l}} = {a \over {\sqrt {h + k + l}}}
The differences a − a0 of (111) crystal plane are given by the following relation [6]:
a - {a_0} = {d_{hkl}}\sqrt {h + k + l}
where a0 is the standard lattice parameter of NiO (standard a0 = 0.4176 nm). The crystallite size of (111) crystal plane for the fabricated NiO thin films was calculated from the Scherer's formula [7]:
G = {{0.9\lambda} \over {\beta \,cos\,\theta}}
where G is the experiment crystallite size, β is the FWHM and θ is the diffraction angle peak (see Table 1).
Results and Discussion
In this article, we have estimated the crystallite size (G) by fitting relationships between the structural parameters (β, a and a − a0), which is detected in the following empirical relationship:
G = {C_1}{a \over \beta} - {C_2}{{a - {a_0}} \over \beta}
where C1 and C2 are constants as C1 = 0.365 and C2 = 0.02. The results of this fitting are given in Table 2.
The crystallite size G experimental and correlated at several deposition temperatures.
Deposition temperature Ts (°C)
Experimental crystallite size (nm)
Fitting crystallite size (nm)
380
19.13
19.14
400
18.74
18.84
420
16.88
16.96
440
18.31
18.45
460
20.72
20.82
Figure 1 shows the variation of the experimental and fitting of the crystallite size at several deposition temperatures in the range of 380–460°C. The measured values of the crystallite sizes were obtained using Eq. (5), which were given in Table 2. This correlation indicated that the crystallite sizes of the NiO thin films can be predominantly influenced by the FWHM β, the lattice parameter a and the differences in a − a0 of the NiO thin films. As seen, all estimated values of crystallite sizes are proportional to the experimental data. Thus, the measurement of the crystallite size values by this proposed model is compatible with practical measurements qualitative. This attribution can be observed with the variation of FWHM β (see Figure 2). This observation was investigated to demonstrate that the calculation of the crystallite size can be influenced by the measurements of the structural parameters (β, a and a − a0).
Conclusions
In this article, the direct correlation of the crystallite size from the experimental values was investigated by a fitting model wherein the calculated crystallite size of the pure NiO thin films was detected in the structural parameters, such as the FWHM β, the lattice parameter a and the differences in a − a0. The experiment data of NiO thin films were prepared at several deposition temperatures in the range of 380–460°C. All estimated values of crystallite sizes are proportional to the experimental data. Thus, the measurement of the crystallite size values by this proposed model is compatible with practical measurements qualitative.