The atomistic model of electronic properties of Al2O3 and ZnO for the calculations of Al-doped ZnO.

The final aim of this work is to simulate the electronic properties of Al-doped ZnO (AZO). The density-functional theory with the Coulomb interaction potential (DFT+U) method was used to specify the electronic properties of wurtzite ZnO: band structure and the density of states. The tool for structural and electronic simulation was QuantumATK, produced by Synopsys. The first part of the simulation was based on the modeling of the wurtzite ZnO periodic cell, which consisted of 108 atoms. We tried to get reasonable value of the band structure, which is from 3.30 to 3.37 eV according to experiments. The implementation of the Hubbard U method requires setting up accurate energy values for localized atomic orbitals. These values will help to establish an estimate of the Al-doped ZnO parameters. The same process was applied to Al2O3-α (corundum) in the second step. Based on this procedure, we have obtained estimated energy values for the 2p orbital for oxygen, the 3p orbital for aluminum, and the 3d orbital for zinc. AZO is used in solar cells as a transparent conducting layer. The percentage of the aluminum doping in ZnO does change its electrical and optical properties. If we can succeed in finding the appropriate percentage of aluminum for the doped material in the model, we can compare it with the experiment and use it in the photovoltaic systems as a transparent conductive layer.


Introduction
As every human does for this world, we also do our best to improve humans' lives.But at the same time, we are trying to pay attention to keeping other properties, such as economic and ecological, at reasonable values and levels.One of the most popular research projects in the last few decades has been about photovoltaics and their efficiency.In our work, we touched on one part of solar cells, which is the conducting layer on the front side of the cells.In our paper, the material that was preferred and the thoughts of improvements were on Al-doped ZnO, which is not a very new topic but still the topic on which research and work are going by scientists.Nowadays, there are several reasons, such as price, the possibility of low-temperature growth, scalability on large substrates, and the most important required transparent conducting layer (TCO) parameters, that give us the possibility of tending to grow Al-doped ZnO as a conducting layer.According to transparency (above 80% in the visible light range) and resistivity, AZO film is very close to another conducting layer such as Indium Tin Oxide (ITO), and therefore AZO can be useful as a transparent conducting layer [1].To establish the AZO electronic and optical parameters, we use the atomistic model.

The computational method
Zinc oxide (ZnO) is widely used as an oxide with a large band gap (~ 3.4 eV), high conductivity with the transition of 3d electrons, good transparency, and high electron mobility [2,3].In our model, we use the wurtzite periodic cell of ZnO (Figure 1) with 108 atoms (3×3×3 structure for X×Y×Z directions, respectively) with initial simulation lattice constant values: a = 3.2495 Å, b = 3.2495 Å, and c = 5.2069 Å.We tried to create these combinations using the relevant method in simulation.The preferred method was the GGA (Generalized gradient approximation) method with a Hubbard U implementation.There is a probability that the d orbital of zinc and the p orbital of the oxygen atom can hybridize, which can affect the electronic structure and bonding characteristics of the Zn-O compound.Therefore, the binding energy in the d orbital of ZnO, especially, cannot be underestimated.GGA and LDA (Linear density approximation) methods without Hubbard U do not have the ability to calculate this probability accurately [4].For example, in one part of Xingua's and co-workers' work [5], they tried without the Hubbard U method and got only 0.74 eV energy in the band structure.A Linear Combination of Atomic Orbitals (LCAO) calculator was a starting point of the computational setup.The unpolarized spin polarization method was chosen for electron spin polarization according to the reference [6], which supposes ZnO as the non-magnetic material.The Perdew-Burke-Ernzerhof (PBE) implementation of the generalized gradient approximation (GGA) was preferred rather than the local density approximation (LDA) for exchange-correlation in our simulation [7].The norm-conserving Fritz-Haber-Institute (FHI) pseudopotential method and Double Zeta Polarized basis sets were chosen to reduce the computational complexity of electronic structure, electron-electron, and electron-ion interactions.The broadening temperature was set to 294 K as a room temperature.One of the critical parameters is the cutoff energy, which was calibrated to 120 Ha (1 Ha = 27.21eV) [4].After different attempts, we have kept a 2×2×2 k-point mesh under the Monkhorst Pack method to define a set of points in the Brillouin zone.After several tries to find the right values for the Hubbard U method, some energy values for the atomic orbitals were estimated: we have stayed with U # = 7 eV for the oxygen atom and U $ = 10 eV for the zinc atom [8].For the Al-doped ZnO, we need to know about the energy values of Al for localized orbitals to set up AZO.Therefore, Al % O & -α, or corundum by another name, was used to learn about electronic properties, especially how much energy the electrons need to transfer between localized orbitals.The main duty was to keep the same method as we had done for ZnO modeling: the same broadening temperature, cutoff energy, and energy values for the localized orbital of oxygen.Under these conditions, we have played with the energy values for localized orbitals of Al.This process has been done on a corundum molecule consisting of 30 atoms total (12 atoms are Al, 18 atoms are O), as shown in figure 2. We have decided on 11 eV of energy values for the 3p-orbital of aluminum after many tries of calculation.

Results and discussion
Previous experimental results, which are 3.3 eV [9] and 3.37 eV [10] measured by X-ray spectroscopy and UV-VIS spectroscopy, respectively, helped us determine the band gap energy of ZnO.As shown in figure 3 (Density of states) and figure 4(a), our result for band gap energy is 3.33 eV at the Γ point.To find the energy values of the localized orbitals of Al, we compared our band gap energy results of α-Al₂O₃ with other people's experiments and computational results.One of the nearest band gap energies we got was 6.11 eV (we have 6.14 eV band gap energy too, but with a 293K broadening temperature), which is near the value of other previous works: 6.3 eV [11], 6.26 eV [12], 6.4 eV [13], and 6.045 eV [14].The result is shown in figure 4(b).

Conclusion
If it is supposed that the simulation part of work on Al-doped ZnO consists of two steps, it is possible to say we have done the first step.We have successfully gotten the results of band gap energy for ZnO and aluminum oxide; nevertheless, the different parameters and even the different simulation systems could give mismatched outcomes.So far, in different publications, we can see some energy values for atomic orbitals for Zn and oxygen and different cutoff energies, which are two of the most important parameters.But we integrated those different possibilities and applied them to our work.In Al₂O₃, especially under the same conditions, it is extra hard to determine the energy value of the atomic orbital for aluminum.But after over 100 simulation tries, we succeeded in obtaining valuable results according to the similarity of the energy band gap diagram with previous experimental results.This work can assist in future calculations of AZO.The application of the right parameters of setup and the right energy values of atomic orbitals can indicate the electrical parameters of AZO with different doping rates of aluminum and even with different amounts of defects made inside the bulk.It is even possible to exchange aluminum with different elements to see the difference in electrical properties.We have already started our work in the Al-doped ZnO direction, and we believe we will amalgamate our simulation results with our own experimental results and compare them in the near future.

Figure 3 .
Figure 3.The density of states of ZnO via QuantumATK software.