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# Open Physics

### formerly Central European Journal of Physics

Editor-in-Chief: Seidel, Sally

Managing Editor: Lesna-Szreter, Paulina

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Volume 14, Issue 1

# The calculation of the optical gap energy of ZnXO (X = Bi, Sn and Fe)

Said Benramache
• Corresponding author
• Material Sciences Department, Faculty of Science, University of Biskra, Biskra 07000, Algeria, B.P. 145 University of Biskra, Biskra 07000, Algeria
• Email
• Other articles by this author:
/ Boubaker Benhaoua
Published Online: 2016-12-30 | DOI: https://doi.org/10.1515/phys-2016-0080

## Abstract

In this paper, a new mathematical model has been developed to calculate the optical properties of nano materials a function of their size and structure. ZnO has good characterizatics in optical, electrical, and structural crystallisation; We will demonstrate that the direct optical gap energy of ZnO films grown by US and SP spray deposition can be calculated by investigating the correlation between solution molarity, doping levels of doped films and their Urbache energy. A simulation model has been developed to calculate the optical band gap energy of undoped and Bi, Sn and Fe doped ZnO thin films. The measurements by thus proposed models are in agreement with experimental data, with high correlation coefficients in the range 0.94-0.99. The maximum calculated enhancement of the optical gap energy of Sn doped ZnO thin films is always higher than the enhancement attainable with an Fe doped film, where the minimum error was found for Bi and Sn doped ZnO thin films to be 2,345 and 3,072%, respectively. The decrease in the relative errors from undoped to doped films can be explained by the good optical properties which can be observed in the fewer number of defects as well as less disorder.

Keywords: ZnO; Thin film; Semiconductor doping; Correlation

PACS: 02.30.Vv; 68.55.ag; 78.20.Bh; 81.40.Tv

## 1 Introduction

Zinc oxide (ZnO), as one of the most important functional semiconductor oxide nanostructures, has a single crystal phase which crystallizes in the hexagonal wurtzite structure (WZ) with lattice parameters: a = 0.3249 nm, c = 0.5206 nm; belonging to the space group P63mc, and is characterized by two interconnecting sublattices of Zn2+ and O2–, such that each Zn ions is surrounded by a tetrahedral of O ions, and vice-versa [14]. Transparent conducting oxides (n-TCO) materials like ZnO based thin films have gained much interest in science and technology. They are usually prepared on glass substrates for opto-electrical devices because of its low resistivity, high optical transparency, good optical gap energy, as well as excellent adhesion to substrates and chemical stability. Due to the excellent structural and optical properties of doped films, ZnO has been used in a wide variety of applications such as transparent electrodes, ferromagnetism, semiconductors, piezoelectric, optoelectronic, solar cells, spintronics and nanodevices [116]. ZnO is one of the most important binary II-VI semiconductor compounds is a natural n-type electrical conductor with a direct energy wide band gap of 3.37 eV at room temperature, a large exciton binding energy (60 meV) [17,18].

ZnO thin films can be produced by several techniques such as reactive evaporation and thermal annealing [19], mol-ecular beam epitaxy (MBE) [20], magnetron sputtered techn-ique [21], pulsed laser deposition (PLD) [22], the low-temperature solution method [23], potentiostatic electrodeposition [24], the sol-gel technique [25], chemical vapor deposition, electrochemical deposition [26] and spray pyrolysis [27].

In this work, we have studied a new model to estimate the optical gap energy of undoped and doped ZnO thin films, which were studied as a function of the Urbach energy, solution molarities and the doping level of films. The investigation focuses on the specific of different doping shows of Bi, Sn and Fe doped ZnO films due to good transparency properties and they provide a range of different values of direct band gaps to obtain a good agreement between the experimental data and correlated optical gap values.

## 2 Experimental and Methods

To Investigate a new calculate of nanomaterials depends on the size, structure and controlled optical properties, it is shown in the growth mechanism and growth parameters. In this study, the undoped and doped ZnO samples were deposited on glass substrates using the ultrasonic spray and spray pyrolysis techniques. In general, the depositions were performed at a substrate temperature of 350°C. The optical band gap energy and the Urbach energy of undoped and Bi, Sn and Fe doped ZnO thin films were taken from the literature [2844], which studied the effect of precursor molarity, doping level and substrate temperature on structural, electrical and optical properties of undoped and doped ZnO thin films with Bi, Sn and Fe.

Table 1 shows the typical procedures of experimental research designs, which used zinc as a precursor. All experimental data of undoped and Bi, Sn and Fe doped ZnO thin films are presented in Tables 2, 3, 4, and 5, respectively, the differences in the experimental data can be explained by differences in the deposition circumstances, such as reactor geometry, substrate temperature, deposition time, flows, concentration of ZnO solution, annealing temperature, etc. As can be seen, the optical gap energy and Urbach energy of undoped and doped ZnO thin films were varied in a nonlinear form. Note that the model proposed of undoped ZnO thin films with precursor molarity as expressed as [38,39].

Table 1

The parameters conditions were used in this research

Table 2

The parameters conditions used in this research

Table 3

Summary results of experimental data and the correlate optical gap energy for Bi doped ZnO thin films.

Table 4

Summary results of experimental data and the correlate optical gap energy for Sn doped ZnO thin films.

Table 5

Summary results of experimental data and the correlate optical gap energy for Fe doped ZnO thin films.

The band gap energy of Bi, Sn and Fe doped ZnO thin films can be calculated with point crucial of precursor molarity of undoped films and doping levels; the ZnO exhibit a single crystals n-type semiconductor with a high crystallinity.

## 3.1 Undoped ZnO Thin Films

Firstly, for undoped ZnO thin films, the optical gap energy was calculated using a nonlinear form by varying the Urbach energy and precursor molarity, found the following relation, as expressed as [38,39]: $Eg=aMEub$(1)

where Eu is the Urbach energy, Eg is the band gap energy correlate, M is the precursor molarity (see Table 2), and a and b are empirical constants as a = 3.28711 and b = 0.0184683.

## 3.2 Doped ZnO Thin Films

For the Bi, Sn and Fe doped ZnO films, the correlation to calculate the optical gaps energies were based on Eq. (1) with X0 = 0 wt.%. To perform the correlation in this step the optical parameters were measured with their doping levels. The correlation can be written in another form: $Eg=a(1+AX0)MEu(b(1+BX0))$(2)

where a and b are empirical constants calculated according to Eq. (1), A and Β are empirical constants related by the doped films, and X0 is the concentration of doping of Bi, Sn and Fe doped ZnO films, presented in Table 3, 4 and 5.

## 3.3 The Relative Error Measurement

In order to compare the obtained models with practical results used in this experiment, a relative error value is used, which is measured between the experimental data and correlated by the following relationship: $ϵ=(EgExp.−EgCor.)EgExp.×100%$(3)

where EgExp. and EgCor. are the experimental and correlated values of optical gap energy, respectively, ϵ is the relative error.

## 4 Results and Discussion

Figure 1 shows the variation of experimental and correlated optical gap energy for undoped ZnO thin films. The correlated values were scaled according to Eq. (1), these results are shown in Table 2, which was estimated as a function of solution molarity and Urbach energy. It can be seen that all estimate values are proportional to the experimental data. Thus, the calculation by the proposed equation is in qualitative agreement with the experimental data, it is shown that the correlation coefficient is high at 0.97, which the maximum agreement of the estimation was found to be minimum in error. As shown in Figures 2, 3 and 4 (see Tables 3, 4 and 5), show the evolution of doping levels Bi, Sn and Fe of doped ZnO thin films on the calculation of optical gap energy, respectively. It are presented as a function of Urbach energy according to Eq. (2), which were have a different empirical constants A and Β as presented in Tables 3, 4 and 5. As can be seen, all correlation coefficients are higher than 0.94, for the Sn doped ZnO thin film is highest, compared to the other dopants and undoped films. It can also be seen that the calculation values are in qualitative agreements with the experimental data, which the maximum agreement of the estimation was found to be minimum relative error. The correlation coefficient depends on both relative errors and doping via:

Figure 1

The variation of optical gap energy experimental and correlate of undoped ZnO thin films.

Figure 2

The variation of optical gap energy experimental and correlate of Bi doped ZnO thin films.

Figure 3

The variation of optical gap energy experimental and correlate of Sn doped ZnO thin films.

Figure 4

The variation of optical gap energy experimental and correlate of Fe doped ZnO thin films.

$R=1−∑iNϵiN$(4)

where N is the number of measurement and ϵ is the relative error. Figures 5 and 6, show the relative errors of optical gap energy of undoped and doped thin films, respectively. For the undoped film all relative errors are smaller than 4%, however, it was found that the relative error of the optical gap energy of doped films are improved with the maximum enhancement of minimum error of Bi and Sn doped ZnO thin films at 2,345% and 3,072%, respectively. It can be seen that these models are suitable for calculation of optical properties of ZnO thin films with varying of some parameters. The decrease in the relative error of undoped to doped films can be explained by the good optical properties which can observe in fewer defects and less disorder.

Figure 5

The variation of error value calculates of optical gap energy of undoped ZnO thin films.

Figure 6

The variation of error value calculates of optical gap energy of Bi, Sn and Fe doped ZnO thin films.

## 5 Conclusion

In summary, the undoped and Bi, Sn and Fe doped ZnO films were taken from the literature, which were deposited on glass substrates using the ultrasonic spray and spray pyrolysis technique. The model proposed to calculate the band gap energy of undoped and doped ZnO thin films were investigated. The relation between the experimental data and theoretical calculations with precursor molarities suggests that the band gap energy is predominantly estimated by the Urbach energy, concentration of ZnO solution and doping level. The measurements by these proposed models are in qualitative agreement with the experimental data, it is shown that the high correlation coefficients were found in the range 0.94–0.99. Thus it is shown that the relative error for undoped film in all calculations are smaller than 4%, however, it was found that after calculating the relative error of the optical gap energy of doped films are improved which the maximum enhancement of minimum error was found at Bi and Sn doped ZnO thin films with 2,345% and 3,072%, respectively. It was confirmed that these models are suitable for calculation of optical properties with varying of some parameters. The decrease in the relative errors of undoped to doped films can be explained by the good optical properties which can be observed in the fewer defects and less disorder.

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Accepted: 2016-09-29

Published Online: 2016-12-30

Published in Print: 2016-01-01

Citation Information: Open Physics, Volume 14, Issue 1, Pages 714–720, ISSN (Online) 2391-5471,

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