Study on the correlation between crystallite size and optical gap energy of doped ZnO thin film

Abstract

In the present paper, we have studied a new approach to the description ofcorrelation between the optical and structural properties of ZnO thin films withdoping levels of Al, Co, and In. The doped zinc oxide thin films were depositedusing ultrasonic spray technique on a glass substrate at 350°C. Thecorrelation between structural and optical properties with doping level suggeststhat the crystallite size of the films is predominantly estimated by the bandgapenergy and the concentration of Al, Co, and In. Also, the gap energy of dopedfilms was estimated by the crystallite size and doping level. The measurement inthe crystallite size and optical gap energy of doped films with correlation isequal to the experimental data. The minimum error value was estimated in dopedZnO thin films with indium and cobalt. Thus, results indicate that such Co-dopedZnO thin films are chemically purer and have many fewer defects and lessdisorder, owing to an almost complete chemical decomposition.

Findings

Background

Zinc oxide has a wurtzite structure, which is a hexagonal crystal structure(lattice parameter: a = 0.325 nm,c = 0.521 nm), belonging to the space group P63mc, and ischaracterized by two interconnecting sublattices of Zn²⁺ andO^2-, such that each Zn ion is surrounded by a tetrahedra of Oions and vice versa [1]. ZnO which is one of the most important binary II-VI semiconductorcompounds is a natural n-type electrical conductor with a direct energy widebandgap of 3.37 eV at room temperature and a large exciton binding energy(approximately 60 meV) [2–5].

ZnO thin films can be doped with a variety of semiconductors to meet the demandsof several application fields. Stoichiometric ZnO films are highly resistive.Conducting films can be made either by creating oxygen vacancies, which act asdonors, or by doping with various dopants such as Ga³⁺,Mn⁴⁺, Al³⁺, In³⁺, Co²⁺, andV³⁺[6–11]. Many attempts were reported about doped ZnO films, but most of themare related with Al doping. There are several works that use dopants such as Co,In, or Al in ZnO to enhance the optical and electrical conductivity. The dopedfilms can be used for various applications such as transparent electronics,piezoelectronic devices, gas sensors, and the transparent electrode window layerof thin-film solar cells [8–13]. The films (ZnO:Al) are considered to be utmost important materialsdue to their high conductivity, good transparency, and lower cost.

The aim of this paper is to study the possibility of the correlation between theoptical and structural properties of ZnO thin films with doping level. Ramana etal. [14] found that the grain size of V₂O₅ thin filmsproduced by pulsed laser ablation strongly influences their opticalcharacteristics. Bensouyad et al. [15] describe the relation between structural and optical properties ofTiO₂:ZnO thin films in a considerate experimental study andcontrolled the variation of crystallite size by modifying the annealingtemperature, film thickness, and doping. Therefore, Cuong Ton-That et al. [16] estimated the direct correlation between the bandgap and crystalstructure and suggest that the band edge optical properties of Mn-doped ZnO arepredominantly influenced by the amount of Mn atoms substituting Zn on thelattice sites. However, similar works have investigated the dependence ofphysical properties of a ZnO thin film as a function of parameter conditionssuch a temperature, thickness, oxidizing conditions, nitrogen addition, anddoping for characterizing the thin films [17–25].

The aim of our paper is to present a new approach to calculate the crystallitesize by the optical gap energy and doping level of a doped ZnO thin film. Also,we have estimated the relationships between the optical gap energy and thecrystallite size with doping level of doped ZnO thin films. Detailedcalculations are developed from doped ZnO thin films with Al, Co, and In.

Methods and model

The ZnO, ZnO:Al, ZnO:Co, and ZnO:In samples were deposited on glass substratesusing ultrasonic spray technique at a temperature of 350°C with 2 min ofdeposition time. The optical gap energy and crystallite size of the films weremeasured with doping level. In our papers, we have studied the effect of variousparameters such as doping level, growth times, substrate temperature, andannealing temperature of the ZnO thin films [26–31] (see Table 1).

Table 1 E _g and G of ZnO, ZnO:Al, ZnO:Co, and ZnO:In as a function of Alconcentration[26]-31]

The correlation between the structural and optical properties of doped ZnO thinfilms was investigated in two parts. First, we studied the optical gap energyand doping level. Second, we estimated a correlation with crystallite size andthe doping level for the optical gap energy, wherein ZnO was doped by variouselements such Al, Co, and In and the element concentration was changed to get adoping limitation.

The correlation parameters for the crystallite size (G), bandgap energy(E _g ), and doping level X ₀ of doped ZnO thin films resulted from the following equation:

$$\left\{\begin{array}{l}{G}_{\left(*\right)}=\frac{G_{\left(\mathrm{e}\right)}}{G_{\left(\mathrm{e}\right)\mathrm{Max}}}\\ E_{g\left(*\right)}=\frac{E_{g\left(\mathrm{e}\right)}}{E_{g\left(\mathrm{e}\right)\mathrm{Max}}}\\ X_{0\left(*\right)}=\frac{X_{0\left(\mathrm{e}\right)}}{X_{0\left(\mathrm{e}\right)\mathrm{Max}}},\end{array}\right.$$

(1)

where G_(e), E_g(e), and X_0(e) are the experimental data; G_(e)Max, E_g(e)Max, and X_0(e)Max are maximal experimental values; and G_(*), E_g(*), and X_0(*) are the first values that have been calculated in thecorrelation relationships.

Results

Correlation with crystallite size

The doped ZnO thin films were deposited for the precursor molarity equal to 0.1M. In this point, the doping level is equal to zero for undoped ZnO thin films.Therefore, we have estimated the relationships between the crystallite size andthe bandgap energy with doping level as the following empiricalrelationships:

$$\left\{\begin{array}{l}{G}_{\left(\mathrm{c}\right)}=a\times E_{g\left(*\right)}^b\times X_{0\left(*\right)}{c}^{}\mathrm{if}{X}_0>0\\ G_{\left(\mathrm{c}\right)}=1.4442\times 10{}^{-4}\times 6,627{}^{E_{g\left(*\right)}}\mathrm{if}{X}_0=0\end{array}\right.,$$

(2)

where a, b, and c are empirical constants and dependon the dopant. These parameters are collected in Table 2 and estimated as a function of dopant element. Table 3 present the correlate values.

$$\mathrm{ZnO}:\mathrm{Al}{G}_{\left(\mathrm{c}\right)}=0.963\times E_{g\left(*\right)}^{19.67}\times X_{0\left(*\right)}{-0.035}^{}$$

$$\mathrm{ZnO}:\mathrm{Co}{G}_{\left(\mathrm{c}\right)}=1.038\times E_{g\left(*\right)}^{19.32}\times X_{0\left(*\right)}{0.092}^{}$$

$$\mathrm{ZnO}:\mathrm{In}{G}_{\left(\mathrm{c}\right)}=1.227\times E_{g\left(*\right)}^{9.657}\times X_{0\left(*\right)}{0.033}^{}$$

Table 2 Variation of empirical constants estimated byEquations 2 and 3 of ZnO:Al, ZnO:Co, andZnO:In

Table 3 G and E _g of ZnO:Al, ZnO:Co, and ZnO:In as a function of doping level

Correlation with optical gap energy

In this part, we have studied the correlation between the optical gap energy andthe crystallite size with doping level. The formula studied in the correlationwith crystallite size is based on a nonlinear correlation; however, we havechosen the complex equation to correlate the optical gap energy as the followingempirical relationships:

$$\left\{\begin{array}{l}{E}_{g\left(\mathrm{c}\right)}=exp(a\prime \times (ln{G}_{\left(*\right)}-\left(b\prime \times ln{X}_{0\left(*\right)}+c\prime \right)\left)\right)\\ \mathrm{if}{X}_0>0\\ E_{g\left(\mathrm{c}\right)}=0.11365ln{G}_{\left(*\right)}+1.00498\\ \mathrm{if}{X}_0=0\end{array}\right.,$$

(3)

where a′, b′, and c′ are empiricalconstants and depend on the dopant. These parameters are collected inTable 2 and estimated as a function of dopantelement.

$$\begin{array}{l}\mathrm{ZnO}:\mathrm{Al}{E}_{g\left(\mathrm{c}\right)}=exp(0.04978\\ \times \left(ln{G}_{\left(*\right)}-\left(-0.04295\times ln{X}_{0\left(*\right)}-0.02884\right)\right))\end{array}$$

$$\begin{array}{l}\mathrm{ZnO}:\mathrm{Co}{E}_{g\left(\mathrm{c}\right)}=exp(0.05176\\ \times \left(ln{G}_{\left(*\right)}-\left(0.09271\times ln{X}_{0\left(*\right)}+0.03759\right)\right))\end{array}$$

$$\begin{array}{l}\mathrm{ZnO}:\mathrm{In}{E}_{g\left(\mathrm{c}\right)}=exp(0.03386\\ \times \left(ln{G}_{\left(*\right)}-\left(0.7691\times ln{X}_{0\left(*\right)}+1.096\right)\right))\end{array}$$

Discussion

In this study, we will show the evolution of the doping level on the crystallite sizeand optical gap energy. We tried to establish correlations for each model proposed.In our calculations, the crystallite size and optical gap energy of doped ZnO thinfilms were estimated from Equations 2 and 3; the ZnO films exhibiting singlecrystals are n-type semiconductors with a high crystallinity.

As shown in Figures 1, 2, and 3, significant correlation was found between the crystallitesize and the optical gap values of the doped ZnO thin films as a function of Al, Co,and In concentration, respectively. The increase of the crystallite size has beenindicated by the enhancement of the crystallinity and c axis orientation ofZnO thin films by Zhu et al. [25]. The measurement in the crystallite size of doped films byEquation 2 is equal to the experimental data; thus, the error of thiscorrelation is smaller than 13% and can be calculated from the relationship|(G_Exp - G_Corr)/G_Exp| × 100. The minimum error value was estimated in thecobalt- and indium-doped ZnO thin films (see Figure 4).

Figure 1

Experimental crystallite size and correlation of ZnO:Al thin films as afunction of Al concentration.

Figure 2

Experimental crystallite size and correlation of ZnO:Co thin films as afunction of Co concentration.

Figure 3

Experimental crystallite size and correlation of ZnO:In thin films as afunction of In concentration.

Figure 4

Error variation of crystallite size of doped ZnO thin films as a functionof doping level. The error variation was estimated byEquation 2.

The maximum enhancement of the crystallite size was found to be of minimum errorafter doping at 3 wt.% (see Figure 4). The amount of Al,Co, and In doping contents achieved in doped ZnO film is 3 wt.%. Based on theexperimental and correlation values for the crystallite size that were developed,good agreement was found between the calculated and experimental values.

The variation of optical gap energy with doping level calculated by Equation 3is shown in Figures 5, 6, and 7 and shows that the optical gap energy can be estimated usingcrystallite size data by varying the doping level in all films. The finalcorrelation data show that the errors calculated from Equation 3 are smallerthan those from Equation 2, as shown in Figure 8. Ascan be seen, the minimal error is achieved in Co-doped ZnO thin films and limited to0% in all concentrations.

Figure 5

Experimental optical gap energy and correlation of ZnO:Al thin films as afunction of Al concentration.

Figure 6

Experimental optical gap energy and correlation of ZnO:Co thin films as afunction of Co concentration.

Figure 7

Experimental optical gap energy and correlation of ZnO:In thin films as afunction of In concentration.

Figure 8

Error variation of optical gap energy of doped ZnO films as function ofdoping level. The error variation is estimated byEquation 3.

We know that such ZnO:Co and ZnO:In thin films are chemically purer and have manyfewer defects and less disorder, owing to an almost complete chemical decomposition,and contain higher optical bandgap energy; thus, we have obtained a minimum errorwith crystallite size from Equation 2.

We have estimated the crystallite size and optical bandgap of doped films usingvarious elements such as Al, Co, and In. The element concentration was changed toget a doping limitation. As can be noted, the ZnO thin film considers a highertransition tail width between the conduction band and valence band. FromEquation 3, it can be concluded that the optical gap is affected by thecrystallite size of undoped and doped ZnO thin films. Thus, the correlation betweenthe crystallite size and the bandgap with the doping level was investigated.

Conclusion

In this paper, we have presented a new approach to the description of correlationbetween crystallite size and optical gap energy with doping levels of Al, Co, andIn. The following conclusions can be drawn from the results presented:

• The correlation between the crystallite size and the bandgap withdoping levels of Al, Co, and In was investigated.

• The crystallite size of the films is predominantly estimated by thebandgap energy and the concentration of Al, Co, and In. Also, the gap energy ofdoped films was estimated by the crystallite size and doping level.

• The measurement in the crystallite size and optical gap energy ofdoped films with correlation is equal to the experimental values.

• The error of correlation of the crystallite size is smaller than14%; the minimum error achieved for ZnO:Co and ZnO:In is limited to 0%. However, forthe correlation of the optical gap energy, the error found is smaller than 2%.Co-doped ZnO films have a minimal error limited to 0%.