3.1 Structural Properties
In order to evaluate the validity of the experimental data, we firstly performed an optimization of the optimum structures of pure ZnO, Yb doped ZnO with various Yb concentrations. The calculated lattice parameters a, c and c/a for the optimized pure ZnO are respectively, a = 3.249 Å, c = 5.216 Å, and c/a = 1.605 which are in good agreement with the experimental values [(Farhat et al. 2018; Bouhouche et al. 2018; Naik et al. 2020; Achehboune et al. 2021), and in good agreement with other theoretical calculations (Khuili et al. 2020; Meng et al. 2017), indicating that our calculations are reliable and prove the validity of our model.
Table 1 shows a summary of the structural parameters of ZnO doped with different concentrations of Yb. It was observed that the lattice parameters a and c increased with increasing Yb concentration, and consequently, the unit cell volume was increased. This result is consistent with another theoretical result (Khuili et al. 2020), as well as the successful preparation in experimental results (Senol 2016). This can be due to the difference in ionic radius between Yb (0.87 A°) and Zn (0.74 A°), contributing to crystal lattice expanding due to the distortion of the crystal lattice, the increase in volume cell is due to the repulsion between Zn and Yb, which produces additional cell volume expansion. The total energy values showed that the geometric configuration of the pure ZnO is that of the most stable structure. The Zn–O bond length decreased slightly with increasing Yb content, whereas the Yb-O bond length decreased with increasing Yb concentration. Furthermore, the Mulliken charge determines the amount of electron density sheared within such a crystal lattice by an atom, in which more positive values mean that more electrons are contributed by the associated atom. This indicates that the Yb dopant contributes more electrons than Zn because of the Mulliken charge values for Yb that are more positive than those of Zn, and the actual values of the charge interaction Yb-O are higher than those of Zn-O.
Table 1
Calculated cell parameters, volume, total energy, bond length, and Mulliken charges of pure ZnO, and ZnO doped with various Yb concentrations.
|
Cell parameters
|
|
|
Bond length (A°)
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Mulliken charges
|
|
a (A°)
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c (A°)
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Volume (A°3)
|
Total energy (eV)
|
Zn-O
|
Yb-O
|
Zn
|
Yb
|
O
|
Pure ZnO
|
3.249
|
5.216
|
47.719
|
-4292.7
|
2.00517
|
-
|
0.81
|
-
|
-0.81
|
Zn0.958Yb0.0417O (4.17%)
|
3.287
|
5.262
|
49.235
|
-4685.2
|
2.02700
|
2.19983
|
0.82
|
0.80
|
-0.81
|
Zn0.937Yb0.0625O (6.25%)
|
3.309
|
5.351
|
50.761
|
-4880.54
|
2.04431
|
2.19913
|
0.81
|
0.79
|
-0.81
|
Zn0.875Yb0.125O (12.5%)
|
3.343
|
5.378
|
52.08
|
-5466.38
|
2.03831
|
2.18398
|
0.82
|
0.78
|
-0.80
|
3.2 Electronic Properties
Band structure
To study the effect of Yb doping concentrations, we have firstly calculated the band structure of pure ZnO. Figure 2a shows the calculated band energy structure of pure ZnO. As observed, pure ZnO exhibits a direct band gap; the valence band maximum and the conduction band minimum are located at the G point of the Brillouin zone. An estimated 0.74 eV band gap of pure ZnO was achieved using only DFT calculations, which is far from the experimental value of 3.37eV (Özgür et al. 2005). In several studies (Yao et al. 2012; Xia et al. 2014; Farooq et al. 2016; Wen et al. 2018), the estimated energy band gap of ZnO using only GGA is between 0.74 and 0.81 eV. The underestimation of the band gap is provided by the strong p-d coupling. To correct this underestimation, we used GGA + U to affect the inaccurate description of strongly localized electrons. Therefore, the GGA + U method can help us to obtain more accurate optical properties. The calculated optical band gap for pure ZnO is 3.38 eV, which is in line with results reported in the experiment and other theoretical calculations [Ma et al. 2013; Obeid et al. 2019; Wang et al. 2020). The results of the band structures of pure and Yb doped ZnO with various concentrations are illustrated in Fig. 2. It can be observed from the Fig. 2b-d that the structures have a direct band gap whose value increases with increasing Yb concentration. It has been determined that Zn0.9583Yb0.0417O, Zn0.9375Yb0.0625O and Zn0.875Yb0.125O, band gaps are 3.40 eV, 3.65 eV and 3.84 eV, respectively, which are wider than pure ZnO. This is consistent with the experimental findings of Ref. (López-Mena et al. 2020) which attributed the increase in the optical band to the lengths of the reduction in the Zn-O bond lengths. Moreover, new occupied states appeared between the conduction band and the Fermi level attributed to the 4f orbitals of the Yb dopant, which are slightly shifted to lower energy as we increase the Yb concentration. It is also clear that the Yb-doped ZnO system is an n-type degenerate semiconductor because of the Fermi level that enters the conduction band to varying degrees and also due to the donor states created close to the conduction bands. A similar behavior was observed in (Daksh and Agrawal 2016; Wen et al. 2018; Wang et al. 2020). The introduction to Yb ions in ZnO system caused the band gap to increase due to the Burstein–Mott effect (Burstein 1954; Moss 1954).
Density of states
Further insight into the contributions of different states to the energy bands is given by the total state density (TDOS) and partial state density (PDOS). Figure 3 presents the total density of states (TDOS) and partial density of states (PDOS) of the pure ZnO and Yb-doped ZnO system. It can be observed from Fig. 3a that the valence band of pure ZnO is mainly composed of the 3d state of Zn and the 2p state of O and the conduction band is mainly composed of the 4s state of Zn and the 2s state of O. The valence band located between − 15.5 and 0 eV is divided into three parts. Within the range of -5.4 to 0 eV, it is mainly composed of O 2p with a minor contribution from the Zn 3d states, resulting in d-p coupling. On the other hand, the valence bands within the range of 8.7 to 5.4 eV are mainly composed of Zn 3d and partial O 2p states. Lastly, an isolated band in the range of -15.5 to -13.8 eV at the valence band is formed with O 2s state. The composition of conduction bands, on the other hand, is consistent with the total density of ZnO in that they are mainly formed by the Zn 4s and O 2p states. For the ZnO doped with Yb shown in Fig. 3b-d, we observe that the valence band shifted towards low energies compared to pure ZnO and continues to shift with increasing amount of Yb. It was also observed that the PDOS of Yb-doped ZnO systems present occupied states at near Fermi level, which mainly come from the Yb-4f orbital. Moreover, the conduction band mainly results from Yb-5d and O-2p orbitals. Consequently, the band structure and DOS show that the increase of Yb doping concentration causes the Fermi level to shift to the conduction band and the DOS to move to lower energy, and the existence of occupied states around the Fermi level will basically determine the optoelectronic characteristics of these materials, indicating that doping with Yb can obtain a high-quality n-type ZnO.
3.3 Magnetic Properties
The partial density of states (PDOS) with spin polarization was performed for all materials in order to illustrate the magnetic mechanism and the effect of Yb as dopant in ZnO with different Yb concentrations. As shown in Fig. 4, the spin-up and spin-down of the total density of states of undoped ZnO were symmetric, indicating that ZnO is a non-magnetic material; the calculated total magnetic moment of pure ZnO is 0.00018 µB. However, for 4.17% of Yb-doped ZnO it is noticed that the spin-up and spin-down channels were asymmetrical and show that Yb-doped ZnO has a ferromagnetic property with an optimal concentration of 4.17%, which exhibiting magnetism behavior in ZnO-YbZn system. It is clear from the figure that there is a clear spin polarization between the partial DOS of the two spin channels near the Fermi level due to spin polarization of 4f electrons of Yb atom (inset image); the total magnetic moment was found to be increased to 0.048 µB. However, as the concentration increased up to 6.25%, the spin up and spin down became symmetrical, and the magnetic moment of the doped ZnO structure was increased; this behavior can be explained by the increase in the antiferromagnetic superexchange interaction along with Yb doping as a result of the decrease in the distance between the Yb ions. In addition, these two system show an n-type degenerate semiconductor as shown from Fig. 2. The calculated total magnetic moment became 0.0087, 0.0052 µB for 6.25% and 12.5% respectively. These current findings show the characteristics of diluted magnetic semiconductors (DMSs) and can help with the design and preparation of new ZnO-based magneto-optoelectronic applications.
3.4 Optical Properties
Dielectric Function
The imaginary part of the dielectric function is a critical characteristic of the optical properties of any material, which can explain the energy required for the electrons to transit from the valence band to the conduction band. Figure 5 illustrates the imaginary parts of the dielectric functions of pure ZnO, Yb-doped ZnO with different concentrations of Yb. As can be seen in Fig. 5, pure ZnO has three main peaks in ε2(ω), which is in good agreement with the experimental results (Hengehold et al. 1970) and the theoretical calculations (Wang et al. 2020). The first peak around 5eV comes mainly from transition between the Zn3d and O2p orbitals. The second peak energy around 10 eV comes from transition between Zn-3d and O-2s orbitals and the third one around 15eV correspond to the transitions of Zn 4p state to O 2p state.
For Yb-doped ZnO systems, we can find that the main dielectric peaks around 15 eV are significantly weakened and shift to lower energies with increasing Yb concentration, indicating that the range of absorption frequency narrows and the average optical transmittance increases. However, the peak around 10 eV increases with increasing Yb concentration due to the strong hybridization between the Zn-3d and O-2s orbitals. Furthermore, compared to the dielectric function spectrum of pure ZnO, Yb-doped ZnO has a new peak around 1 eV which decreases and shifted to higher energies with increasing Yb concentration, It is the same behavior as that of iɛ2(ω) in (Jin et al. 2016; Wang et al. 2020) which, according to the study of state density and band structure, can be attributed to the transition of the Yb 4f states to the Zn 4s states. Therefore, all the photons having a low energy can be absorbed by the doped ZnO, which relatively increased the absorption coefficient in the visible light region.
Absorption, reflectivity and transmittance
Figures 6 shows the calculated absorption and reflectivity of pure and Yb-doped ZnO with different concentrations of Yb. As can be seen from Fig. 6a, the pure ZnO has an absorption peaks around 350 nm which gradually reduced and shifted toward the higher energy region with increasing Yb concentration. Meanwhile, in the visible light range of 500–800 nm, the absorption of Yb-doped ZnO was relatively enhanced compared to that of pure ZnO. This can be attributed to the Yb-4f defect induced near the conduction band minimum. Figure 6b shows the reflectivity of pure and Yb doped ZnO with deferent Yb concentrations; it can be observed that all pure and Yb doped ZnO structures have a low reflectivity which is less than 0.08 in the visible range. Compared to pure ZnO, the main peak about 400 nm is blue-shifted. A further decrease in the reflectivity spectrum was observed for Yb-doped ZnO in the visible region.
Refractive index
Figure. 8 shows the behavior of the refractive index (n) and the extinction coefficient (k) of ZnO and Yb-doped ZnO in the wavelength range of 200–800 nm; which is obtained from the relationship between the complex dielectric function and the complex refractive index. As shown in Fig. 8(a), the static value of the refractive index n(0) at 0 eV of pure ZnO was 1.59 and the values of 1.92, 1.65 and 1.75 belonged to 4.17%, 6.25% and 12.5% of Yb, respectively. Furthermore, a higher refractive index was obtained for pure ZnO with value 1.72 at 250 nm and 410 nm. As we can see, the static refractive index has changed considerably with increasing Yb. As the Yb concentration increases, the refractive index has changed considerably and shifts to higher energies with a maximum value of 1.76 obtained at 260 nm for 12.6% of Yb. However, in the visible range 380-780nm, the refractive index decreased. This is consistent with the experimental findings of Ref. (López-Mena et al. 2020) which suggest that the decrease in the refractive index can be associated with variations in carrier concentration. Figure 8b shows the extinction coefficient (k) for pure ZnO and Yb-doped ZnO. A decrease in the extinction coefficient from 200 to 450 nm is observed. While the opposite behavior is observed for wavelengths from 405 to 800 nm; this can be attributed to the impurity state induced by Yb doping, which in line with the calculation results of band structure and calculated transmittance observed in Fig. 3 and Fig. 7.