In the current work, lattice parameters, band structure, and optical characteristics of neat and doped ZnO are studied by utilizing ultrasoft pseudopotentials (USP) and generalized gradient approximation (GGA) with the support of First-principles calculation (FPC) derived from density functional theory (DFT). The measurements had been performed in the supercell geometry that had been optimized. To discover the lattice parameters, electronic band structure, and optical characteristics of V-doped ZnO, the FPC based on DFT has been applied in CASTEP. The calculated lattice parameters are agree with observed experimental data. The volume of the doped system grows as the content of V-doping in it increases. Pure and doped ZnO were investigated for band structure and energy bandgaps using the Monkhorst-Pack scheme's k-point sampling techniques in the high symmetry direction of the Brillouin zone (G-A-H-K-G-M-L-H). In the presence of high V content, the bandgap energy decreases from 3.331 to 2.055 eV. From the band E-K diagram (V.B and C.B), PDOS and DOS diagrams insight into the electronic structure of the atom and the amount to which each energy band contributes to a specific atomic orbital were specified. The bandgaps were manipulated so that they narrowed, resulting in a redshift of the absorption spectrum in the IR region. The imaginary and real parts of the extinction coefficient, refractive index, and dielectric function have all increased at lower photon energies.

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- (Hameed Majid Advanced Polymeric Materials Research Lab., Physics Department, College of Science, University of Sulaimani, Qlyasan Street, Sulaimani 46001, Kurdistan Regional Government, Iraq )
- (Department of Civil engineering, College of Engineering, Komar University of Science and Technology, Sulaimani 46001, Kurdistan Regional Government, Iraq)

## I. INTRODUCTION

There are uses of ZnO semiconductors in several fields, including gas sensors, surface
acoustic wave devices, transparent contacts, and biomedical materials. The outstanding
characteristics of ZnO-based semiconductors are the direct bandgap (BG) of 3.37 eV
with a considerable binding energy of exciton. These are well-known suitable photonic
materials in ultraviolet and visible regions. The rationalization of designing modern
optoelectronic devices relies on direct BG manipulation in an attempt to create barrier
layers and quantum wells in device heterostructures ^{[1]}. Nowadays, zinc oxide has attracted attention because of an appropriate direct BG
of zinc oxide (ZnO) of 3.37 eV, comparable to GaN semiconductor material. At room
temperature, ZnO experiences relatively large exciton energy (60 meV) compared to
GaN semiconductors ^{[2-}^{4]}. The ZnO semiconductor is a well-known material characterized by non-toxicity, low
cost, and abundant resources. Fig. 1 shows the three varieties of Zinc oxide crystals: rock salt, zinc blende, and wurtzite
structures.

The most prevalent ZnO phase at room temperature and pressure is wurtzite, but the
zinc-blende structure can only be stable on cubic substrates. The unit cell in these
two structures is a tetrahedron with five atoms; one atom belongs to$~ \mathrm{Zn}^{+2}$
and is surrounded by four $\mathrm{O}^{-2}$, and vice versa ^{[5]}. The hexagonal unit cell's lattice parameters measured by X-ray diffraction under
ambient circumstances are $c=~ 5.2069\mathrm{A}^{\mathrm{o}},$ $a=~ 3.2495\mathrm{A}^{\mathrm{o}}$,
and the density is equal to $5.605\mathrm{g}/\mathrm{cm}^{3}$, and the axial ratio
$(c/a$) is equal to $1.603$ ^{[6,}^{7]}.

The tetrahedral interaction between Zn$^{+2}$ and O$^{-2}$ ions causes polar symmetry
along the hexagonal axis. Currently, in optical and mechanical manufacturing of devices,
ZnO has widely been utilized ^{[8]}, including Light Emitting Diode ^{[9,}^{10]}, Lasers ^{[11]}, optoelectronic devices ^{[12]}, photocatalysis ^{[13]}, solar cells ^{[14,}^{15]}, optoelectronic devices ^{[16]}, gas sensor ^{[17]}. This is owing to the wide BG of ZnO, which provides it weakly susceptible to visible
light; thereby, only ultraviolet light has been absorbed. Additionally, its conductivity
and the number of carriers are modest ^{[18]}.

The doping of transition metal into ZnO enables it to be applicable in optical and
mechanical applications. As stated in the literature, various experimental investigations
of the optical and structural characteristics of transition metals and vanadium (V)
doped ZnO have been documented. S. Maensiri, et al. ^{[19]} dealt previously with the V-doped ZnO in terms of structural and optical properties
using the sol-gel method. The study verified that the BG of the V-doped ZnO samples
was reduced upon the addition of V. Wang et al. ^{[20]} used both x-ray photoelectron spectroscopy and energy dispersive spectroscopy (EDS)
to examine the structural and optical properties of V-doped ZnO. It was established
that V-doping causes all films to have a wurtzite structure and grow mostly along
the c-axis. The films' transmittance was measured in the calculation of the optical
properties. Gherouel et al. ^{[14]}, examined the optical and structural characteristics of V-doped ZnO using spray pyrolysis
for various controlled concentrations (1-5\%) of V element. The BG energy varied between
3.17 and 3.25 eV, corresponding to the vanadium quantity. Within the 300-1800 nm range
of optical transmission and reflectance spectrum for each V-doped ZnO sample, maximum
transparency (80-90\%) was recorded in the visible range. Abaira et al. ^{[21]}, performed optical and structural characteristics of V-doped ZnO by the sol-gel technique.
It was concluded that the doping of V from (2-10\%) makes the BG wide. The study of
optical properties has shown that the presence of vanadium widens the optical BG.
It is observed that both structural and optical characteristics of doped ZnO samples
have extensively been identified from a theoretical standpoint. Changlong Tan et al.
^{[15]}, carried out optical and structural characteristics of Cd-doping ZnO. The prediction
of the BG of a Cd-doped ZnO monolayer was documented using first-principle DFT in
terms of the Hubbard U + local density approximation (LDA) method. Looking at the
negative sign of energy formation of the doped sample, it is emphasized that the Cd
incorporation sample is chemically stable.

Jianfeng et al. ^{[22]} reported the Cu/Al-doped ZnO systems with optical characterization using the FPC
plane-wave pseudopotential method in the generalized gradient approximation in conjunction
with the Hubbard U correction based on DFT. Co-doping is the method of choice to reduce
the BG of ZnO, consequently causing the absorption edge of the systems to undergo
red-shifting and possessing the greatest absorption in the visible light region. To
explore the structural, electronic band structure, and optical characteristics of
V-doped ZnO, the FPC based on DFT has been implemented in CASTEP ^{[23]}. Based on the approach, insight into the optical properties of V doping in ZnO at
the microscopic scale is achieved. From the energy calculation, it is predictable
to quantify the lattice energy of the V incorporation at the Zn replacement site.
The pure ZnO possesses wide BG energy, and the direct BG upon V doping has been obtained.
Also, the creation of new levels at the G (gamma) point has been verified, leading
to an upward shift of the valence band (VB). Additionally, a substantial BG lowering
occurs upon V doping. A state relocation to higher energy can be detected from the
density of states diagram. Redshifts as the optical properties of ZnO are observed
as a consequence of V doping within-host lattice.

## II. THEORETICAL MODELS AND CALCULATION METHODS

### 2.1 Theoretical Models

The hexagonal system is the crystal structure of wurtzite ZnO, with the space group
of P63mc. In the structure, each zinc ion is surrounded by four oxygen ions and also
the three parameters of the unit cell are as follows: $a=b=3.249\mathrm{A}^{\mathrm{o}}$,
$c=5.205\mathrm{A}^{\mathrm{o}}$ ^{[6]}. To make the experimental results consistent, the supercells $Zn_{1-x}V_{x}O$, $3\times
2\times 2$, $2\times 2\times 2$, and $2\times 2\times 1$ have been established corresponding
to $4.1\% $, $6.2\% $, and $12.5\% $ doping, where V atoms can replace Zn atoms. Fig. 2 shows the proposed supercells.

### 2.2 Calculation Method

Taking the DFT into consideration and aiming at the plane-wave-pseudo potential (PWP)
approach, the first-principles calculations have been carried out using the CASTEP
code. The computations were based on DFT, as applied in the Materials Studio package's
CASTEP software ^{[23]}. The fast calculation is the major feature of the applied approach because of its
relatively high efficiency in which, in advances, approximating the shape of the orbitals
is absent. The assumption is that the core of the ions is both inner electrons and
nuclei; on the other hand, the valence electrons will interact and thus assure fast
convergence of ion-electron potential. For electron-ion interaction investigation,
the ultrasoft pseudopotential (USP) has been applied in addition to generalized gradient
approximation (GGA) and the electron exchange interaction proposed by Perdew-Burke-Ernzerhof
(GGA-PBE) ^{[23,}^{24]}. The PWP method relies strongly on an assumption of governing almost all physical
and chemical characteristics of solids and molecules by valence electrons. This attempt
rationalizes the real atoms as pseudo atoms; wherein just the valence electrons are
involved in the self-consistent calculation (i.e., neglecting the impact of core electrons
in the calculation). Therefore, the cost of computational calculation reduces considerably
^{[25]}. The exchange and correlation energy possess impact; herein, it has been dealt with
within the GGA ^{[26]}. The certain valence electronic configuration used in the current calculation is
$\mathrm{Zn}\colon 3d^{10}4s^{2}$, $\mathrm{V}\colon 3d^{3}4s^{2}$, and $\mathrm{O}\colon
2s^{2}2p^{4},$for the materials in a reciprocal space form.

After the self-consistent process, the structure's total energy converges, the force
exerted on the atoms is smaller than 0.03 eV/nm, and the stress deviation is less
than 0.05 GPa. Just to take into consideration, the K points of the Brillouin zone
are $5\times 5\times 4$ ($1\times 1\times 1$ unit cells); $3\times 2\times 3$, ($2\times
2\times 1$, $2\times 2\times 2$, and $3\times 2\times 2$, supercells). The first optimization
was the crystal structure, followed by the electronic structure and total and partial
densities of state. Afterward, the optical characteristics have been specified using
the outcomes obtained from the structural parameters. The accurate description of
the electronic structure of oxides doped with transition metal V and localized oxygen
components is quantitatively performed from the GGA+U ^{[27,}^{28]}. However, apparent limitations of DFT in GGA make the bandgap to be lower than the
experimental value (3.37~eV) ^{[1]}. Furthermore, the energy calculation for the first Brillouin zone has been carried
out by implementing the special k-point sampling techniques of the Monkhorst-Pack
scheme ^{[29]}. The total energy of different k-point grids has been computed for all compounds
to reach a satisfying mesh to ensure the accuracy of the whole results. The electronic
structure was modified by GGA+U for all systems in this study, the energy of the 2p
level of O and the 3d level of Zn take the values Ud, Zn =10 eV, Us, Zn = 0 eV, Up,
Zn = 0, and Up, O = 7 eV ^{[2]}, respectively.

## III. RESULTS AND DISCUSSION

### 3.1 Lattice Parameters Study

A common theoretical tool used to determine crystal structure is the geometry optimization
procedure. Full geometrical optimizations on the atomic positions or cell parameters
are carried out as presented in Table 1. In the theoretical calculations, only a single crystal structural data of the compound
of interest have been taken into account. For example, the pure ZnO, ($a=b=3.2492\mathrm{A}^{\circ}$
and $c=5.2054\mathrm{A}^{\circ}$, $c/a=1.602$) found these lattice parameters are
quite in agreement with the following experimental values; ($a=b=3.25\mathrm{A}^{\circ}$,
$c=5.207\mathrm{A}^{\circ}$, $c/a=1.602$) with the variance of less than $2\% $ ^{[20]}. Despite this, the predicted lattice parameters and unit cell volumes were somewhat
out compared with the experimental findings published in the literature (within 2
percent). On the other hand, satisfactory agreement with the existing theoretical
[17, 27, 30, 31] findings has been attained. It's worth noting that the GGA approximation
has a built-in tendency to overestimate lattice parameters. As long as the computations
are as accurate as they need to be, these types of mistakes are acceptable. Another
interesting feature of the data is the tiny amount of variance between the theoretical
and experimental values. First-principles computations are accurate as a consequence.
The volume and lattice parameters of the ZnO system in the a and c axes increase as
the quantity of V$^{5+}$ ions in doping is increased. The doped system's lattice properties
and volume are somewhat higher than those of the parent ZnO system. This is caused
by the indigence to calculate the electronic structure properties in which the lattice
parameters are impacted.

In calculating the BG of most systems, the limitations involved in the GGA approximation, make the BG calculations to be as not reached the level of reflecting the actual results. Another cause of the present results is the repulsive interactions of the extra electrons of the V$^{5+}$ ion that exists effectively. As a result of both factors' impact, the volume of the doped sample rises as the amount of V-doping increases. And also in Table 1. Different doping elements present various impacts on the changing rate of the lattice parameters a and c. and the ratio between them floats up and down.

##### Table 1. The lattice parameters of pure ZnO and doped ZnO for different elements after geometry optimization

### 3.2 Band Structure and Density of State Studies

The work conducted in this research specified the band structure along a high symmetry direction of the Brillouin zone (G-A-H-K-G-M-L-H) for pure ZnO and V-doped ZnO. When determining a material's characteristics, it is crucial to accurately determine its density of states (DOS) and its bandgap structure. In addition, the likelihood of electrons occupying certain energy ranges may be calculated from the shape of the electronic band (that is, energy bands). As a result, the bandgap refers to the unusable energy ranges. The electronic BG may be measured in insulators and semiconductors by comparing the valence band maximum (VBM) with the conduction band minimum (CBM). The electronic band structure computations will be useful in determining the probable transition of electrons from VBM to CBM. Intuitively, the valence band lies below the Fermi state $\left(E_{F}\right)$ at 0 eV, and the CB locates above the BG energy.

From Fig. 3, a direct G-to-G transition BG energy of 3.331 eV for super-cells including, $\mathrm{Zn}_{0.9583}V_{0.04166667}O$
and $\mathrm{Zn}_{0.9375}V_{0.0625}O$ and the band structure calculated along the
symmetry direction of the Brillion zone (G-A-H-K-G-M-L-H) are recorded. Located at
the G point, the valence and conduction bands have a straight $G-to-G$ transition.
This suggests the existence of p-type semiconductors of $\mathrm{Zn}_{0.9583}V_{0.04166667}O$
and $\mathrm{Zn}_{0.9375}V_{0.0625}O$. It is principally accepted that the direct
nature of the BG contains a transition of an electron from the valence band to the
conduction band without phonons assistance which is mostly free of losing incident
energy during transitions. The bottom 10 bands (occurring around -9 eV) are related
to $\mathrm{Zn}\colon 3d$ levels. The next 6 bands from -5 eV to 0 eV correspond to
$\mathrm{O}\colon 2p$ bonding states ^{[33,}^{34]}. Based on the DFT approach obtained in the current work it is possible to design
doped ZnO with direct BG. The BG energy was reduced from 3.331 eV for neat ZnO to
2.055 eV for ZnO dopped with 12.5 percent of V atom. Ultimately, the direction of
the Brillouin zone was (G-A-H-K-G-M-L-H), and the direct $G-to-G$ transition of the
supercell $\mathrm{Zn}_{0.875}V_{0.125}O,$ evidence formation of p-type semiconductors.

This model tells that the BG can be reduced to the energy of $2.055\mathrm{eV}$. Fig. 3(a) demonstrates that the value of the direct band in parent ZnO is lower than that of the experimental value (3.37 eV).In other words, the theoretical values of the BG energy are lower than the experimental values in all cases. This might be due to the lack or poor description of strong Coulomb correlation and exchange interaction between electrons. Notably, the prominent notice is that the calculated BG of the present and previous studies are in good agreement, as presented in Table 2.

The DOS and partial density of states (PDOS) of both parent $ZnO$, $\mathrm{Zn}_{0.9583}V_{0.04166667}O$, $\mathrm{Zn}_{0.9375}V_{0.0625}O$, and $\mathrm{Zn}_{0.875}V_{0.125}O$ supercells are plotted and exhibited in Fig. 4. Overall, introducing the V atoms into the lattice results in existing of primarily $\mathrm{O}\colon 2s^{2}2p^{4}$ state, $\mathrm{V}\colon 3\mathrm{d}^{2}$ in the top of valence, forming $V-O$ bonds besides $Zn-O$ bonds. In Fig. 4, PDOS was applied to analyze the electronic structure deeply providing a contribution of the energy bands in a specific atomic orbital.

In parent ZnO, both $\mathrm{Zn}\colon 3d^{10}4s^{2}$, and $\mathrm{O}\colon 2s^{2}2p^{4}$ states contribute mainly to the valance bands between ${-}$5.5 and 0 eV, and $\mathrm{Zn}\colon 3d^{10}4s^{2}$, $\mathrm{V}\colon 3d^{3}4s^{2}$, and $\mathrm{O}\colon 2s^{2}2p^{4}$ states are involved in the conduction bands ranging between 3.318 and 12.4 eV. For super-cells, there are additional contributions of $\mathrm{V}\colon 3d^{3}4s^{2}$ states. The localized $\mathrm{V}\colon 3d^{2}$ energy energy state substitutes dopant V ions for Zn, localizing within the Fermi level between -0.7 and 0.5 eV. The presence of $\mathrm{V}\colon 3d^{3}4s^{2}$ also also within, the energy gap from 1.6 to 3 eV reduces the energy gap. The existence of these states between 4 to 8~eV is evidenced. Consequently, the PDOS of all these states increases with increasing the quantity of V in the doping process.

##### Fig. 3. The E-K (Band Structure) diagram for (a) ZnO; (b) $\mathrm{Zn}_{0.9583}\mathrm{V}_{0.04166667}\mathrm{O}$; (c) $\mathrm{Zn}_{0.9375}\mathrm{V}_{0.0625}\mathrm{O}$; (d) $\mathrm{Zn}_{0.875}\mathrm{V}_{0.125}\mathrm{O}$.

##### Fig. 4. The PDOS and total DOS for (a) ZnO; (b) $\mathrm{Zn}_{0.9583}\mathrm{V}_{0.04166667}\mathrm{O}$; (c) $\mathrm{Zn}_{0.9375}\mathrm{V}_{0.0625}\mathrm{O}$; (d) $\mathrm{Zn}_{0.875}\mathrm{V}_{0.125}\mathrm{O}$.

##### Table 2. The direct bandgap energy of pure ZnO and doped ZnO for different elements after geometric parameters optimization

### 3.3 Optical Properties

Crystals' band structure and optical qualities are reflected in the dielectric function,
which may be considered the point at which electronic transition and electronic structure
meet. The solid-state technique states that the complex dielectric function $\varepsilon
\left(\omega \right)=\varepsilon _{1}\left(\omega \right)+i\varepsilon _{2}\left(\omega
\right)$ can express the optical properties of semiconductor materials ^{[36]}. On the one hand, the imaginary part results from transitions between the CB and
the VB. Calculating momentum matrix components for filled and non-filled levels and
Kramers-Kronig dispersion relations theoretically yields both the real $\varepsilon
_{1}\left(\omega \right)$ and imaginary $i\varepsilon _{2}\left(\omega \right)$ portions
of dielectric functions, respectively ^{[36,}^{37]}. According to quantum mechanics, the system's photon-electrons interact through time-dependent
disturbances in the system's ground electronic state. The absorption or emission of
photons triggers transitions between occupied and unoccupied states in a quantum system.
In terms of DOS, excitation spectra may be thought of as a conduction-valence band
DOS ^{[38]}. Furthermore, from $\varepsilon _{1}\left(\omega \right)$ and $i\varepsilon _{2}\left(\omega
\right)$, extraction of other optical properties is obtainable. The optical properties
from the density functional theory are achievable, for instance, the dielectric function,
absorption coefficient, and refractive index ^{[12]} equation (1,2,3,4,5) ^{[12,} ^{31,} ^{38-}^{41]}.

##### (1)

$$ \varepsilon _{1}\left(\omega \right)=\frac{2}{\pi }\rho _{0}\int _{0}^{\infty }\frac{\omega '\varepsilon _{2}\left(\omega \right)}{\omega '^{2}-\omega ^{2}}d\omega $$##### (2)

$ \varepsilon _{2}\left(\omega \right)=\frac{C}{\omega ^{2}}\sum _{V,C}\int _{BZ}\frac{2}{\left(2\pi \right)^{3}}\left| M_{CV}\left(k\right)\right| ^{2}.\delta \left(E_{C}^{k}-E_{V}^{k}-\mathrm{\hslash }\omega \right)d^{3}k $##### (3)

$ \alpha \left(\omega \right)=\sqrt{2}\omega \left[\sqrt{\varepsilon _{1}^{2}\left(\omega \right)+\varepsilon _{2}^{2}\left(\omega \right)}-\varepsilon _{1}\left(\omega \right)\right]^{\frac{1}{2}} \\ $##### (4)

$ n\left(\omega \right)=\left[\sqrt{\varepsilon _{1}\left(\omega \right)^{2}+\varepsilon _{2}\left(\omega \right)^{2}}+\left(\omega \right)\right]^{\frac{1}{2}}/\sqrt{2} \\ $##### (5)

$ k\left(\omega \right)=\left[\sqrt{\varepsilon _{1}\left(\omega \right)^{2}+\varepsilon _{2}\left(\omega \right)^{2}}-\left(\omega \right)\right]^{\frac{1}{2}}/\sqrt{2} $where $~ \mathrm{\hslash }\omega $ is a photon energy, $k$ is the inverted lattice, respectively. $\omega ~ $ and $\rho _{0}$ are frequency and the density of the medium, respectively. The$\delta \left(E_{C}^{k}-E_{V}^{k}-\mathrm{\hslash }\omega \right)$ represents the delta function imposes energy conservation in the third step corresponding to the electron's escape through the crystalline surface. $\left| M_{CV}\left(k\right)\right| ^{2}$ refers to the momentum transition matrix element between initial and final states. $E_{V}^{k,}$ and $E_{C}^{k}$ are the VBM and CBM energy, respectively.

Fig. 5(a) Show that pure ZnO and V-doped systems ($\mathrm{Zn}_{0.9583}V_{0.04166667}O$; $\mathrm{Zn}_{0.9375}V_{0.0625}O$; $\mathrm{Zn}_{0.875}V_{0.125}O$.) have static dielectric constants of around 2.302, 2.553, 2.572, and 2.657, respectively. The band gap is inversely proportional to the $\varepsilon _{1}\left(0\right)$. As a result, the decrease in the band gap can be attributed to the rise in the static dielectric constant, which is consistent with the results of band structure calculations. The band illustrates that V-doped ZnO has a metallic characteristic, yet the $\varepsilon _{1}\left(\omega \right)$ shows that it is dielectric. $\varepsilon _{1}\left(\omega \right)$ is fluctuated between 0 to 12 eV after that it decreases rapidly to -0.3 at 17.4~eV. Evidence of poor light transmission and energy losses within the media with significant reflection can only be obtained using the negative component of the dielectric constant $\varepsilon _{1}\left(\omega \right)$.

The imaginary part of electronic transitions between occupied and unoccupied states accounts for the peaks of $\varepsilon _{2}\left(\omega \right)$. In Fig. 5(b), we can see that there are three distinct peaks of the $\varepsilon _{2}\left(\omega \right)$ for pure and V-doped ZnO. ZnO's DOS and energy band structure interpretation suggests that the peak at 9.5 eV is mostly the optical response to the transition between the $\mathrm{O}\colon 2p$ (higher valence band) and $\mathrm{Zn}\colon 3d$ (lower conduction band) states. The transitions in the valence band, which are between $\mathrm{Zn}\colon 3d$ and $\mathrm{O}\colon 2p$ states, give rise to the peak at 13.17 eV. Transitions between$~ \mathrm{~ Zn}\colon 4d$ (lower valence band) and $\mathrm{O}\colon 2s$ (lower conduction band) states produce a peak of about 16 eV. The electronic transition between the $V\colon 3d$ states in the higher valence band and the $Zn\colon 3d$ levels in the lowest conduction band produces the first peak of about 5 eV near the energy gap. At the high energy range, the remaining three primary peaks stay in their original locations, indicating that there has been no transition.

It is notable, however, that just the first primary peak has altered its location, indicating that ZnO's low-energy area has been effectively doped. However, even if the final peak is due to a mixed transition, it is seen that the loaded sample not only moves absorption peaks to lower energies but also reduces the sharpness of their appearance. Fig. 5 indicates that the BG has narrowed dramatically, resulting in a reduced absorption edge. V-doped ZnO, on the other hand, results in a decrease in energy BG. The red arrow intersection on photon energy (Fig. 5(b)) gives the energy BG (3.32). It is close enough to that estimated (3.331) from the E-K diagram (Fig. 3(a)) for pure ZnO.

The optical absorption spectrum is the vital tool that is mainly focused on. The absorption
coefficients of ZnO correspond to various quantities of V are presented in (Fig. 6). The absorption edge value is recorded as 0.68~eV, (in agreement with the paper
^{[42]} for pure ZnO, and there are three distinct absorption peaks at 9.89 eV, 13.5~eV,
and 16.12 eV (10.07 eV, 16.87 eV, and 20.69~eV) respectively. The last two peaks are
created by the electronic transition between the O-2p state and Zn-4s state. A red
shift is seen in the absorption of doped ZnO with V compared to parent ZnO at the
lower energy state, originating from the BG reduction. The parent ZnO is not a strong
absorber in the IR region; however, it is a good absorber in the UV region. It is
well-known that the energy of visible light lies between 1.62 and 3.11 eV. From (Fig. 6) we can see that V-doped ZnO has an intense absorption in the ultraviolet region.
The right side of (Fig. 6) shows that the pure and V-doped ZnO has a weak absorption in the visible and infrared
region. The intense absorption in the visible and near-ultraviolet region is because
of the electronic interband transitions in the V-3d states. The electronic intraband
transitions in V-3d and Zn-4s states in the conduction band can cause a weak absorption
in the infrared region (lower photon energy) ^{[36]}. The system has intense absorption at (13.5~eV-16.59 eV) for pure and V-doped ZnO.
The absorption peaks indicate that V-doped ZnO could be a good choice for lasers,
detectors, or diodes in the infrared and vacuum ultraviolet regions.

The refractive index $n\left(\omega \right)$ is an important optical characteristic that allows material transparency to be measured. The calculated refractive index $n\left(\omega \right)$ and extinction coefficient $k\left(\omega \right)$ of undoped, V-loaded ZnO are shown in (Fig. 7). In (Fig. 7(a)) the $n\left(0\right)$ of parent ZnO is around 1.51 and becoming 1.59, 1.60, and 1.62 for ($\mathrm{~ Zn}_{0.9583}V_{0.04166667}O$; $\mathrm{Zn}_{0.9375}V_{0.0625}O$;$\mathrm{Zn}_{0.875}V_{0.125}O$), respectively after doping. The refractive index in the visible region increases with increasing V concentration. The refractive indices are smaller in the deep ultraviolet band (8-11 eV). Because electrons in the deep level orbital are sheltered by electrons in the shallow level during the transition, electrons in the deep level orbital have a harder time transitioning in the orbit, resulting in a lower refractive index. when it shifts to the higher energy level the refractive index becomes 0.65 at 18.5 eV. As demonstrated in (Fig. 5(b)) the computed imaginary part $\varepsilon _{2}\left(\omega \right)$ of the dielectric constant of undoped and V-doped ZnO are similar. The extinction coefficient $k\left(\omega \right)$ for $\mathrm{Zn}_{0.875}V_{0.125}O$ at the first increase slowly with rising the photon energy but parent ZnO, $\mathrm{Zn}_{0.9375}V_{0.0625}O$ and $\mathrm{Zn}_{0.9583}V_{0.04166667}O$ remains unchanged. We can use the $k\left(\omega \right)$ to determine the energy band gap of the systems.

## IV. CONCLUSIONS

In conclusion, a first-principles implementation is necessary to assess the structural, E-K diagram, and optical features of the neat and V-doped ZnO systems. According to the calculated results, the BG of the pure and doped systems has dropped from 3.318 to 2.055 eV due to the higher V amount. Increases in V have modified the optical transition between the VBM and CBM. Due to the doping of V, the refractive index, extension coefficient, real and imaginary part dielectric function, and real and imaginary part dielectric function of ZnO are all substantially high in the low energy region. Increased V doping content in ZnO promotes ZnO volume growth. The redshift of the absorption spectrum is enhanced in the IR region when the V content has been increased as an impurity.

## ACKNOWLEDGMENTS

The authors gratefully acknowledge the financial support for this study from the Ministry of Higher Education and Scientific Research-Kurdish National Research Council (KNRC), Kurdistan Regional Government/Iraq. The financial support from the University of Sulaimani is greatly appreciated.

## References

Rezhaw A. Qadir received the B.Sc. degree in general Physics from the University of Sulaimani, College of Education, Iraq, in 2011, and she was a M.S. student in Material Science from the University of Sulaimani, College of Education, Iraq, in 2020. From 2011 to 2019, she was an assistant of a physician in the Department of Physics, College of Education, University of Sulaimani, Kurdistn, Iraq. In august 2022, she joined her college, where she is currently a teacher. Her research interests include structural properties and TDOS/PDOS of Vanadium doped Zinc Oxide.

Dlear R. Saber received the B.Sc. in Physics from Salahaddin University-Erbil in 1990, MSc. and PhD. degrees in Material Science from Baghdad University, Baghdad, Iraq in 2000 and 2009 respectively. He joined Sulaimani University, College of Science, Physics Departments, Kurdistan regional government, Iraq in 1994 and as a member of the academic staff since 2000. His principal research interests have been in the fields of material science, and theoretical material science. He is a member of Iraqi Physics and Mathematics Society.

Shujahadeen B. Aziz is a professor in the Physics department at the University of Sulaimani. He received the B.Sc. degree in Physics from the university of Sulaimnai/ Iraq in 2003, and the M.Sc. degree in Solid State Physics in 2007 from the same university. In 2012, he received his Ph.D. degree in advanced materials from the university of Malaya/ Malaysia. He currently the head of Physics department and a leading researcher at the University of Sulaimani. He is the author or coauthor of more than 215 papers in international refereed journals. His research interests cover several aspects across polymer electrolytes, electrochemical energy storage devices, and composite material characterizations. He has received several important recognitions for his research career, such as being listed in “A standardized citation metrics author database annotated for scientific field” which is awarded by Elsevier BV, Stanford University for the years 2020 and 2021, and the national grant from the ministry of higher education and scientific research-Kurdistan region-Iraq.