# Investigation of Structural, Electronic, and Optical Properties of Chalcogen-Doped ZrS2: A DFT Analysis

Authors: Sayedul Hasan; Mohammad Tanvir Ahmed; Abdullah Al Roman; Shariful Islam; Farid Ahmed
Journal: Advances in Materials Science and Engineering
 (2023)

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## Abstract

The electrical and optical characteristics of a ZrS2 monolayer doped with chalcogen atoms (O, Se, or Te), where dopants are introduced by substituting the S atom, are examined on the basis of the density functional theory. The semiconductors pristine ZrS2 and O, Se, and Te-doped ZrS2 monolayers possessed indirect band gaps of 1.187 eV, 1.227 eV, 1.146 eV, and 0.922 eV, respectively. According to the formation energy, the O-doped ZrS2 monolayer is more stable compared to Se-doped and Te-doped ZrS2 monolayers. The optical properties are very similar for both the undoped and doped ZrS2 monolayers. The absorption coefficient and optical conductivity are the highest in the ultraviolet energy region. The designed materials are potentially suitable for UV photodetection and UV filtering applications.


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## Body

## 1. Introduction

The approach of investigation on two-dimensional (2D) materials, including graphene [1], silicone [2, 3], boron nitride (BN) [4, 5], and transition metal dichalcogenide (TMD) monolayers [6], was sparked by the discovery of graphene in 2004 [7, 8]. A novel generation of transistors, optoelectronic (OE) devices, energy storage, and gas sensors are just a few of the exciting potential for industrial applications that these 2D materials provide, in addition to opening up new fields [6, 9–13]. One of the most robust materials ever tested is graphene, which has sp2-hybridized orbitals and a 2D honeycomb network [14]. Graphene offers a lot of potential for ultrahigh-speed electronics, according to its unique electrical characteristics, such as the quantum Hall effect (half-integer), charge carriers, high migration rates, and saturation velocities [15–19]. However, because graphene has no band gap, it cannot be used in many optoelectronic devices. The band gap of graphene has now been suggested to be opened using a variety of techniques, including the in-plane strain application [20, 21] and external electric field application along with chemical modification [22–24]. In contrast, 2D semiconductor materials made of stacked transition-metal dichalcogenides have a naturally found band gap, and recent developments on field effect transistors (FET) [11] based on a TMD monolayer have drawn intense research attention. A transition metal dichalcogenide (TMD) layer (M) is inserted between two chalcogens (X) layers to form the hexagon, with alternately placed M and X atoms at the corners. Each TMD layer is made up of three atomic layers.These molecular layers in bulk MX2 are kept by the Van der Waals force with a graphite-like Bernal stacking. It is interesting to note that as the dimensionality goes from 3D to 2D, MoX2 and WX2 experience alteration between an indirect band gap and direct band gaps from 1.5 to 2.0 eV [25–28] which are appropriate for optoelectronic (OE) applications and energy harvesting devices [27, 28]. Recently, an experimentally manufactured novel 2D TMD called the ZrS2 monolayer was created [29, 30]. In order to investigate its electrical transport capabilities, high and fast-responsive hexagonal ZrS2monolayer-based FET devices have been synthesized [31]. According to Ahmad et al., ZrS2 nanostructures are potential candidates for high short-circuit current, large-area solar cell applications [32]. However, the lack of thorough study work on doped 2D ZrS2 hinders future improvements and applications. There are still many unknown doped ZrS2 parameters that are crucial for material design, including in-plane stiffness, optical reaction, adsorption coefficients, Poisson’s ratio, and geometrical effect on the band structure. Therefore, there is an urgent need for a theoretical analysis of these features. Moreover, we feel that the doped ZrS2 monolayer merits special consideration given the intricate and adaptable electrical architectures of 2D TMD monolayers.In this study, we focus on the chalcogen-doped ZrS2 monolayer’s structural, electrical, and optical characteristics via the density functional theory (DFT) analysis. Our interest in studying the consequences of dopants on various properties of ZrS2 was inspired by the fact that, to our best knowledge, there has not yet been a thorough exploration of ZrS2 monolayers doped with chalcogen atoms.


## 2. Computational Details

The DFT analysis is performed via the Cambridge Serial Total Energy Package (CASTEP) code [33–35], and for the exchange-correlation correction, the generalized gradient approximation of the Perdew–Burke–Ernzerhof method was utilized [36]. The Broyden–Fletcher–Goldfarb–Shanno (BFGS) minimization algorithm was used to analyze the geometrical parameters by optimizing the pristine ZrS2 and X-doped ZrS2 (X = O, Se, and Te) structures [37]. The plane wave cutoff energy of 600 eV is chosen for the plane wave expansion and the 3×3×1k-points grid is maintained by the Monkhorst–Pack scheme [37]. The tuning of cell parameters as well as atomic positions are performed until the doping of the residual force is below 0.01 eV/Å and till the convergence energy of 2 × 10−5  eV between two stages is reached. Two ZrS2 layers and X-doped ZrS2layers are separated by a distance of 29 Å vacuum region to avoid interlayer interactions. In order to explore X doping in the monolayer of ZrS2, it is designed with a supercell consisting of 3×3×1two-dimensional (2D) unit cells containing 18 sulfur atoms and 9 zirconium atoms where 1 sulfur atom is replaced by X atom, as shown in Figure 1. The valance electrons for Zr, S, O, Se, and Te are 4p6 5s2, 3s2 3p4, 2s2 2p4, 4s2 4p4, and 5s2 5p4, respectively. For each system of doping, S atom is substituted by a dopant atom maintaining the percentage of doping to 3.7%.Figure 1
Optimised structures of the top and side view of the (a) pristine ZrS2 and (b)–(d) O, Se- and Te-doped ZrS2 monolayer, respectively.


## 3. Results and Discussion

### 3.1. Optimized Structures

Figures 1(a)–1(e) show the top and side views of the ZrS2 monolayer and X-doped ZrS2. After total energy relaxation, the results of the optimization of the pristine ZrS2 unit cell of the space group p63/mnc revealed that the calculated lattice constant a is 3.68 Å and the calculated Zr-S bond length is 2.57 Å, which satisfies previous studies [38, 39]. Additionally, one sulfur atom in the pristine monolayer of ZrS2 is replaced by other chalcogen atoms such as O, Se, and Te. The bond length varies and the lattice constant changes very little as a result of chalcogen atom doping concentration. The bond length for O-doped ZrS2 ranges from 2.557 Å to 2.598 Å. Similar to this, for Se-doped ZrS2 and Te-doped ZrS2, the bond length varies from 2.531 Å to 2.593 Å and from 2.559 Å to 2.579 Å, respectively.The lattice constant decreases due to O doping whereas increases after Se and Te doping. This variation occurred due to the variation of the dopant diameter. O ion has a lesser diameter compared to S, Se, and Te, i.e., O occupies a lesser volume compared to other chalcogen ions, which can cause the decrease in the cell volume as well as lattice constants. Hence, the lattice constants can vary with the variation of dopant concentration. Due to 3.7% doping, a slight change in lattice constants is observed. Similarly, the lattice constant increases due to Se and Te doping due to their larger ionic diameter.Table1 lists the specific characteristics, including the computed lattice constants (a), average bond lengths between Zr and the closest S and X atoms (DZr-S and DZr-X, respectively), and the formation energy (EForm). Table 1 demonstrates that the link length rises as atomic radius rises. For O-doped ZrS2, Se-doped ZrS2, and Te-doped ZrS2, the bond length between the nearest Zr and the X-doped atom (DZr-X) is 2.12 Å, 2.69 Å, and 2.93 Å, respectively. The formation energy EForm can be obtained from the following equation [40–43]:(1)EForm=Edoped−Epristine+nμS−μX.Here,Edoped is the total ground state energy of X (X = O, Se, and Te)-doped ZrS2, Epristine is the total ground state energy of the pristine ZrS2, μXandμS represent the chemical potentials of the X (O, Se, and Te) and S atoms, and n is the number of S atoms replaced by O, Se, and Te atoms. From Table 1, we can see that O-doped ZrS2 has the most stable structure and Te-doped ZrS2 has the least stable structure.Table 1
Structural parameters (lattice constants (a), the average bond length between Zr and the nearest S atoms (DZr-S), the bond length between nearest Zr and the X atom (DZr-X), and the formation energy (EForm)) of the pristine and single-doped ZrS2 structure.
X-doped ZrS2a (Å)DZr-S(Å)DZr-X(Å)EForm in eVPristine11.102.570−37.87X = O11.032.58 (2.557 to 2.598)2.12−1.45X = Se11.122.57 (2.559 to 2.579)2.690.82X = Te11.152.56 (2.531 to 2.593)2.931.35


### 3.2. Mulliken and Hirshfeld Charge Analysis

The Mulliken charge analysis not only offers an objective standard for atom-to-atom bonding but also aids in determining if a bond is covalent or ionic. A covalent bond is indicated by a higher bond population, whereas a lower bond population indicates an ionic bond formation. Other facets of the ionic character can be measured using the effective ionic valance, that is, the gap between the conventional ionic charge as well as the Mulliken charge here on anion species. Greater values above zero show an increase in covalency, whereas a value of zero represents the ideal ionic bonding [44, 45]. Mulliken charge analysis has been carried out to observe the charge distribution of the pure and chalcogen-doped ZrS2, and the average Mulliken charge of every element is displayed in Table 2.Table 2
Mulliken and Hirshfeld charges of pristine and chalcogen-doped ZrS2.
SpeciesMulliken charge analysisHirshfeld charge analysisZrS2ZrS2@OZrS2@SeZrS2@TeZrS2ZrS2@OZrS2@SeZrS2@TeS−0.36−0.38−0.36−0.36−0.16−0.17−0.16−0.17Zr0.720.730.720.720.320.320.320.32O−0.73−0.32Se−0.21−0.12Te0.00−0.03Mulliken charge illustrates the partial atomic charges that result from differences in electronegativity inside molecules. When two atoms with different electronegativities combine, the atom with a higher electronegativity attracts the bound electrons, turning it partially negative while turning the other partially positive. The S atom is more electronegative in pure ZrS2, which means it will be partially negative while the Zr atom is partially positive. Chalcogen atoms are more electronegative than the transition metal atom Zr in chalcogen-doped ZrS2. As a result, the Zr atoms are partially positive and the chalcogen atoms are partially negative. Using the Mulliken analysis scheme, these partially positive and negative values are listed in Table 2. After doping X = O, Se, and Te, it is observed that the partially positive and negative charge values of Zr and S atoms have altered, but the charge distribution of the doped ZrS2 sheet has remained almost the same. The interaction of the doped atom causes the electron density in ZrS2 to deform, causing this change.The Hirshfeld population analysis (HPA) scheme divides the deformation density among the atoms of a molecule to express atomic charges [44]. According to the Hirshfeld charge distribution study shown in Table 2, the charge state of Zr is positive, but the charge states of the chalcogen atoms (S, O, Se, and Te) are negative. The partially positive and negative charge values differ between the HPA scheme and the Mulliken scheme because these two analysis schemes are distinct from one another. HPA is less dependent on the basis set than Mulliken charge analysis [46].


### 3.3. Band Structure Analysis

In Figure2, we exhibit the pristine ZrS2 monolayer’s energy band structures and doped ZrS2 monolayer calculated by the PBE method. Figure 2(a) demonstrates that the pure ZrS2 single layer is indeed a semiconducting material with a band gap of 1.187 eV, which is slightly greater than previous theoretical studies [47, 48]. The valance band maximum (VBM) is located at the Γ point, whereas the conduction band minimum (CBM) is located at the Q point of the Brillouin zone.Figure 2
Band structures of pristine and single-doped ZrS2. (a) ZrS2. (b) O-doped ZrS2. (c) Se-doped ZrS2. (d) Te-doped ZrS2.
(a)(b)(c)(d)Figures2(b)–2(d) show the band structures of the X-doped ZrS2 sheet where we substitute one S atom with the same chalcogen group atoms (X = O, Se, and Te). The VBM is located at the Γ point, although the CBM lies at the Q point, which shows the X-doped ZrS2 (X = O, Se, and Te) monolayers with a band gap of 1.227 eV, 1.146 eV, and 0.922 eV, respectively. The band gap is increased for X = O-doped ZrS2 than pristine ZrS2, but the other two X = Se and Te-doped ZrS2 are decreased which means the VB and CB are moved towards Fermi levels (EF), which is described by a reduction of the band gap as the confinement of electrons and holes increases and the size of the doped element decreases [49].


### 3.4. Density of States (DOS) Analysis

By examining the electron energy states close to the Fermi level (EF), DOS analysis is the most fundamental way of determining whether a material is an insulator or a metal. If there is a continuous number of states present in EF, which shows that there is no band gap, then the material will behave in a metallic pattern. On the other hand, the absence of energy levels in EF suggests the existence of a band gap, which suggests that the material in question is either a semiconductor or an insulator.Figure3 shows the results of our analysis of the pristine ZrS2 sheet’s total density of states (T-DOSs) and partial density of states (PDOSs) before and after doping. While the S-3p orbitals have the largest presence in the valance band (VB), the Zr-3d orbitals have the highest contribution to the conduction band (CB) (Figure 3(a)). A situation is very similar to the one shown in Figure 3(b), in which one of the S atoms is replaced by an O atom. However, when the S atom is replaced by Se or Te, the VB is dominated by the S-3p and Zr-4p electrons, while the CB is contributed by the Zr-3d electrons. There is a significant hybridization going on between the Zr-4p states and the S-3p states in both the VB and the CB (Figures 3(c) and 3(d)). According to the results of the T-DOSs, the CBM is further off from the Fermi level in O-doped ZrS2 than in pristine ZrS2. On the other hand, the CBM is closer to the Fermi level in Se- and Te-doped ZrS2 than in pristine ZrS2, and the CBM is furthest near the Fermi level in Te-doped ZrS2.Figure 3
The density of states of the pristine and single-doped ZrS2 monolayers. (a) Pristine ZrS2. (b) O-doped ZrS2. (c) Se-doped ZrS2. (d) Te-doped ZrS2.
(a)(b)(c)(d)


### 3.5. Optical Properties

The dielectric function can be used to calculate frequency-dependent optical properties, such as optical absorption, reflectivity, loss function, and conductivity, where the Kramer–Kronig dispersion relation is used to calculate the dielectric function [50]. The optical properties of ZrS2 and X-doped ZrS2 materials are demonstrated in Figure 4 for energy ranging up to 18 eV. According to Figure 4(a), the absorption (α) explains the absorption of photons per unit distance in the medium [51]. Maximum absorption is found in the ultraviolet energy region. However, all the structures showed a wide and fine absorption in the range of 3–14 eV. The maximum absorption coefficient of the pristine ZrS2 structure of 81733.86 cm−1 at 6.17 eV is observed, which signifies that a fraction of the micron thickness of the ZrS2 is sufficient to absorb most of the incident waves within the given energy range. The corresponding penetration depth for the 6.17 eV photons is about 0.12 μm.Figure 4
Diagrams of the optical parameters (absorption (a), dielectric function (real) (b), dielectric function (imaginary) (c), conductivity (d), reflectivity (e), refractive index (f), and loss function (g)) of pristine ZrS2 and X (X = O, Se, and Te)-doped ZrS2.
(a)(b)(c)(d)(e)(f)(g)Similarly, the maximum value ofα for the Se-doped ZrS2, O-doped ZrS2, and Te-doped ZrS2 is 80898.60 cm−1 at 6.17 eV, 79880.6369 cm−1 at 6.22 eV, and 77192.15 cm−1 at 6.15 eV, which correspond to 0.123 μm, 0.125 μm, and 0.13 μm, respectively. A very slight red shit (blue shift) is observed in the absorption edge at the low energy region for Se-doped ZrS2 and Te-doped ZrS2 (O-doped ZrS2), which satisfies the decrease (increase) of the band gap after doping. The absence of absorption in the 0 eV–1.16 eV range signifies annihilation [52]. These findings indicate that such structures could be used in UV filters and UV photodetectors.Figure4(b) shows the dielectric function (real) ε1ω which represents the polarization of light in a material. It is maximum from near-infrared (0.29 eV) to visible photon (2.31 eV), particularly for green photons at about 2.31 eV. The dielectric function has multiple peaks, which dissipate with increasing photon energy. It drops to a near value of zero value (0.28, 0.35, 0.29, and 0.36) at 6.70 eV for ZrS2 and 6.79 eV, 6.67 eV, and 6.65 eV for X-doped ZrS2 (X = O, Se, and Te), respectively. The energy loss function reports the loss of energy caused by fast-moving electrons through matter. The loss function has a wide variety of prominent peaks for a wide energy range (Figure 4(g)). The plasmonic energy (ℏωp) is shown by the major peak of the loss function diagram. The several energy loss peaks for ZrS2 and X-doped ZrS2 (X = O, Se, and Te) are observed at 1.82, 3.95, 5.90, and 7.48 eV, which correspond to their plasma frequency.Figure4(c) shows the imaginary dielectric function ε2 (ω). From our computed results, the peaks of the imaginary parts of the dielectric function show at visible and UV energy regions. The interband transition from VB to CB is associated with 1.44 eV and 3.12 eV, but the value of the imaginary part of the dielectric constant is a small change for doped ZrS2 monolayers than pristine ZrS2 structures. Figure 4(d) exhibits the conductivity of the pristine and doped structures. It measures the number of free charge carriers generated as a result of bond breakage caused by the electron-photon interaction [53]. For all the structures, it reaches an extreme in the UV energy region. The maximum values are observed at 5.67 eV, 5.76 eV, 5.65 eV, and 5.61 eV for ZrS2 and X-doped ZrS2 (O, Se, and Te), respectively, and the conductance vanishes for higher energies, i.e., the conductivity peak blue shifted after O-doping but red-shifted after Se and Te-doping. This result signifies that comparatively less energy photons are required to achieve maximum conductivity for Te-doped ZrS2. Figure 4(e) describes the reflection of the structures, which is frequency-dependent. When compared to other energies, the minimum absorption for UV photons shows a high reflectivity in this area. Reflectivity represents the fraction of loss of the incident energy via reflection. In the visible energy range, the reflectivity ranges between 0.04 and 0.13 with a maximum in the green wavelength region. In the higher energy region, up to 13.6% of reflection is observed for the pristine ZrS2. Meanwhile, the reflectivity decreased significantly after doping in visible and UV regions.The reflectivity spectra also show red shifting after O-doping and blue shifting after Se and Te-doping. All the structures show very less reflection of incident photons (<14%), which can provide better performance in optoelectronic applications. Since both the reflectivity and refractive indexη represent the lowering of light speed in the medium, curves for η follow the analogous pattern as the dielectric function’s real part, as shown in Figure 4(f). The structures possess a comparatively higher refractive index in the visible energy region. The fact that there is no optical response above 15 eV means that the electronic coupling is low above these energies and that photons above such energies face little to no resistance as they flow through the material.


## 3.1. Optimized Structures

Figures 1(a)–1(e) show the top and side views of the ZrS2 monolayer and X-doped ZrS2. After total energy relaxation, the results of the optimization of the pristine ZrS2 unit cell of the space group p63/mnc revealed that the calculated lattice constant a is 3.68 Å and the calculated Zr-S bond length is 2.57 Å, which satisfies previous studies [38, 39]. Additionally, one sulfur atom in the pristine monolayer of ZrS2 is replaced by other chalcogen atoms such as O, Se, and Te. The bond length varies and the lattice constant changes very little as a result of chalcogen atom doping concentration. The bond length for O-doped ZrS2 ranges from 2.557 Å to 2.598 Å. Similar to this, for Se-doped ZrS2 and Te-doped ZrS2, the bond length varies from 2.531 Å to 2.593 Å and from 2.559 Å to 2.579 Å, respectively.The lattice constant decreases due to O doping whereas increases after Se and Te doping. This variation occurred due to the variation of the dopant diameter. O ion has a lesser diameter compared to S, Se, and Te, i.e., O occupies a lesser volume compared to other chalcogen ions, which can cause the decrease in the cell volume as well as lattice constants. Hence, the lattice constants can vary with the variation of dopant concentration. Due to 3.7% doping, a slight change in lattice constants is observed. Similarly, the lattice constant increases due to Se and Te doping due to their larger ionic diameter.Table1 lists the specific characteristics, including the computed lattice constants (a), average bond lengths between Zr and the closest S and X atoms (DZr-S and DZr-X, respectively), and the formation energy (EForm). Table 1 demonstrates that the link length rises as atomic radius rises. For O-doped ZrS2, Se-doped ZrS2, and Te-doped ZrS2, the bond length between the nearest Zr and the X-doped atom (DZr-X) is 2.12 Å, 2.69 Å, and 2.93 Å, respectively. The formation energy EForm can be obtained from the following equation [40–43]:(1)EForm=Edoped−Epristine+nμS−μX.Here,Edoped is the total ground state energy of X (X = O, Se, and Te)-doped ZrS2, Epristine is the total ground state energy of the pristine ZrS2, μXandμS represent the chemical potentials of the X (O, Se, and Te) and S atoms, and n is the number of S atoms replaced by O, Se, and Te atoms. From Table 1, we can see that O-doped ZrS2 has the most stable structure and Te-doped ZrS2 has the least stable structure.Table 1
Structural parameters (lattice constants (a), the average bond length between Zr and the nearest S atoms (DZr-S), the bond length between nearest Zr and the X atom (DZr-X), and the formation energy (EForm)) of the pristine and single-doped ZrS2 structure.
X-doped ZrS2a (Å)DZr-S(Å)DZr-X(Å)EForm in eVPristine11.102.570−37.87X = O11.032.58 (2.557 to 2.598)2.12−1.45X = Se11.122.57 (2.559 to 2.579)2.690.82X = Te11.152.56 (2.531 to 2.593)2.931.35


## 3.2. Mulliken and Hirshfeld Charge Analysis

The Mulliken charge analysis not only offers an objective standard for atom-to-atom bonding but also aids in determining if a bond is covalent or ionic. A covalent bond is indicated by a higher bond population, whereas a lower bond population indicates an ionic bond formation. Other facets of the ionic character can be measured using the effective ionic valance, that is, the gap between the conventional ionic charge as well as the Mulliken charge here on anion species. Greater values above zero show an increase in covalency, whereas a value of zero represents the ideal ionic bonding [44, 45]. Mulliken charge analysis has been carried out to observe the charge distribution of the pure and chalcogen-doped ZrS2, and the average Mulliken charge of every element is displayed in Table 2.Table 2
Mulliken and Hirshfeld charges of pristine and chalcogen-doped ZrS2.
SpeciesMulliken charge analysisHirshfeld charge analysisZrS2ZrS2@OZrS2@SeZrS2@TeZrS2ZrS2@OZrS2@SeZrS2@TeS−0.36−0.38−0.36−0.36−0.16−0.17−0.16−0.17Zr0.720.730.720.720.320.320.320.32O−0.73−0.32Se−0.21−0.12Te0.00−0.03Mulliken charge illustrates the partial atomic charges that result from differences in electronegativity inside molecules. When two atoms with different electronegativities combine, the atom with a higher electronegativity attracts the bound electrons, turning it partially negative while turning the other partially positive. The S atom is more electronegative in pure ZrS2, which means it will be partially negative while the Zr atom is partially positive. Chalcogen atoms are more electronegative than the transition metal atom Zr in chalcogen-doped ZrS2. As a result, the Zr atoms are partially positive and the chalcogen atoms are partially negative. Using the Mulliken analysis scheme, these partially positive and negative values are listed in Table 2. After doping X = O, Se, and Te, it is observed that the partially positive and negative charge values of Zr and S atoms have altered, but the charge distribution of the doped ZrS2 sheet has remained almost the same. The interaction of the doped atom causes the electron density in ZrS2 to deform, causing this change.The Hirshfeld population analysis (HPA) scheme divides the deformation density among the atoms of a molecule to express atomic charges [44]. According to the Hirshfeld charge distribution study shown in Table 2, the charge state of Zr is positive, but the charge states of the chalcogen atoms (S, O, Se, and Te) are negative. The partially positive and negative charge values differ between the HPA scheme and the Mulliken scheme because these two analysis schemes are distinct from one another. HPA is less dependent on the basis set than Mulliken charge analysis [46].


## 3.3. Band Structure Analysis

In Figure2, we exhibit the pristine ZrS2 monolayer’s energy band structures and doped ZrS2 monolayer calculated by the PBE method. Figure 2(a) demonstrates that the pure ZrS2 single layer is indeed a semiconducting material with a band gap of 1.187 eV, which is slightly greater than previous theoretical studies [47, 48]. The valance band maximum (VBM) is located at the Γ point, whereas the conduction band minimum (CBM) is located at the Q point of the Brillouin zone.Figure 2
Band structures of pristine and single-doped ZrS2. (a) ZrS2. (b) O-doped ZrS2. (c) Se-doped ZrS2. (d) Te-doped ZrS2.
(a)(b)(c)(d)Figures2(b)–2(d) show the band structures of the X-doped ZrS2 sheet where we substitute one S atom with the same chalcogen group atoms (X = O, Se, and Te). The VBM is located at the Γ point, although the CBM lies at the Q point, which shows the X-doped ZrS2 (X = O, Se, and Te) monolayers with a band gap of 1.227 eV, 1.146 eV, and 0.922 eV, respectively. The band gap is increased for X = O-doped ZrS2 than pristine ZrS2, but the other two X = Se and Te-doped ZrS2 are decreased which means the VB and CB are moved towards Fermi levels (EF), which is described by a reduction of the band gap as the confinement of electrons and holes increases and the size of the doped element decreases [49].


## 3.4. Density of States (DOS) Analysis

By examining the electron energy states close to the Fermi level (EF), DOS analysis is the most fundamental way of determining whether a material is an insulator or a metal. If there is a continuous number of states present in EF, which shows that there is no band gap, then the material will behave in a metallic pattern. On the other hand, the absence of energy levels in EF suggests the existence of a band gap, which suggests that the material in question is either a semiconductor or an insulator.Figure3 shows the results of our analysis of the pristine ZrS2 sheet’s total density of states (T-DOSs) and partial density of states (PDOSs) before and after doping. While the S-3p orbitals have the largest presence in the valance band (VB), the Zr-3d orbitals have the highest contribution to the conduction band (CB) (Figure 3(a)). A situation is very similar to the one shown in Figure 3(b), in which one of the S atoms is replaced by an O atom. However, when the S atom is replaced by Se or Te, the VB is dominated by the S-3p and Zr-4p electrons, while the CB is contributed by the Zr-3d electrons. There is a significant hybridization going on between the Zr-4p states and the S-3p states in both the VB and the CB (Figures 3(c) and 3(d)). According to the results of the T-DOSs, the CBM is further off from the Fermi level in O-doped ZrS2 than in pristine ZrS2. On the other hand, the CBM is closer to the Fermi level in Se- and Te-doped ZrS2 than in pristine ZrS2, and the CBM is furthest near the Fermi level in Te-doped ZrS2.Figure 3
The density of states of the pristine and single-doped ZrS2 monolayers. (a) Pristine ZrS2. (b) O-doped ZrS2. (c) Se-doped ZrS2. (d) Te-doped ZrS2.
(a)(b)(c)(d)


## 3.5. Optical Properties

The dielectric function can be used to calculate frequency-dependent optical properties, such as optical absorption, reflectivity, loss function, and conductivity, where the Kramer–Kronig dispersion relation is used to calculate the dielectric function [50]. The optical properties of ZrS2 and X-doped ZrS2 materials are demonstrated in Figure 4 for energy ranging up to 18 eV. According to Figure 4(a), the absorption (α) explains the absorption of photons per unit distance in the medium [51]. Maximum absorption is found in the ultraviolet energy region. However, all the structures showed a wide and fine absorption in the range of 3–14 eV. The maximum absorption coefficient of the pristine ZrS2 structure of 81733.86 cm−1 at 6.17 eV is observed, which signifies that a fraction of the micron thickness of the ZrS2 is sufficient to absorb most of the incident waves within the given energy range. The corresponding penetration depth for the 6.17 eV photons is about 0.12 μm.Figure 4
Diagrams of the optical parameters (absorption (a), dielectric function (real) (b), dielectric function (imaginary) (c), conductivity (d), reflectivity (e), refractive index (f), and loss function (g)) of pristine ZrS2 and X (X = O, Se, and Te)-doped ZrS2.
(a)(b)(c)(d)(e)(f)(g)Similarly, the maximum value ofα for the Se-doped ZrS2, O-doped ZrS2, and Te-doped ZrS2 is 80898.60 cm−1 at 6.17 eV, 79880.6369 cm−1 at 6.22 eV, and 77192.15 cm−1 at 6.15 eV, which correspond to 0.123 μm, 0.125 μm, and 0.13 μm, respectively. A very slight red shit (blue shift) is observed in the absorption edge at the low energy region for Se-doped ZrS2 and Te-doped ZrS2 (O-doped ZrS2), which satisfies the decrease (increase) of the band gap after doping. The absence of absorption in the 0 eV–1.16 eV range signifies annihilation [52]. These findings indicate that such structures could be used in UV filters and UV photodetectors.Figure4(b) shows the dielectric function (real) ε1ω which represents the polarization of light in a material. It is maximum from near-infrared (0.29 eV) to visible photon (2.31 eV), particularly for green photons at about 2.31 eV. The dielectric function has multiple peaks, which dissipate with increasing photon energy. It drops to a near value of zero value (0.28, 0.35, 0.29, and 0.36) at 6.70 eV for ZrS2 and 6.79 eV, 6.67 eV, and 6.65 eV for X-doped ZrS2 (X = O, Se, and Te), respectively. The energy loss function reports the loss of energy caused by fast-moving electrons through matter. The loss function has a wide variety of prominent peaks for a wide energy range (Figure 4(g)). The plasmonic energy (ℏωp) is shown by the major peak of the loss function diagram. The several energy loss peaks for ZrS2 and X-doped ZrS2 (X = O, Se, and Te) are observed at 1.82, 3.95, 5.90, and 7.48 eV, which correspond to their plasma frequency.Figure4(c) shows the imaginary dielectric function ε2 (ω). From our computed results, the peaks of the imaginary parts of the dielectric function show at visible and UV energy regions. The interband transition from VB to CB is associated with 1.44 eV and 3.12 eV, but the value of the imaginary part of the dielectric constant is a small change for doped ZrS2 monolayers than pristine ZrS2 structures. Figure 4(d) exhibits the conductivity of the pristine and doped structures. It measures the number of free charge carriers generated as a result of bond breakage caused by the electron-photon interaction [53]. For all the structures, it reaches an extreme in the UV energy region. The maximum values are observed at 5.67 eV, 5.76 eV, 5.65 eV, and 5.61 eV for ZrS2 and X-doped ZrS2 (O, Se, and Te), respectively, and the conductance vanishes for higher energies, i.e., the conductivity peak blue shifted after O-doping but red-shifted after Se and Te-doping. This result signifies that comparatively less energy photons are required to achieve maximum conductivity for Te-doped ZrS2. Figure 4(e) describes the reflection of the structures, which is frequency-dependent. When compared to other energies, the minimum absorption for UV photons shows a high reflectivity in this area. Reflectivity represents the fraction of loss of the incident energy via reflection. In the visible energy range, the reflectivity ranges between 0.04 and 0.13 with a maximum in the green wavelength region. In the higher energy region, up to 13.6% of reflection is observed for the pristine ZrS2. Meanwhile, the reflectivity decreased significantly after doping in visible and UV regions.The reflectivity spectra also show red shifting after O-doping and blue shifting after Se and Te-doping. All the structures show very less reflection of incident photons (<14%), which can provide better performance in optoelectronic applications. Since both the reflectivity and refractive indexη represent the lowering of light speed in the medium, curves for η follow the analogous pattern as the dielectric function’s real part, as shown in Figure 4(f). The structures possess a comparatively higher refractive index in the visible energy region. The fact that there is no optical response above 15 eV means that the electronic coupling is low above these energies and that photons above such energies face little to no resistance as they flow through the material.


## 4. Conclusion

The structural, optical, and electronic properties of ZrS2 and chalcogen atoms mono-doping ZrS2 are studied using the first-principle methods based on DFT. A slight deformation of the unit cell was observed after doping due to the variation of dopant radius. The minimum formation energy among the doped structures is for O-doped ZrS2 which signifies the most stable structure. All the structures are shown with the CBM and VBM located at Q and Γ points, respectively. The pristine ZrS2 and O, Se, or Te-doped ZrS2 monolayers are indirect band gap semiconductors with band gaps of 1.187 eV, 1.227 eV, 1.146 eV, and 0.922 eV, respectively. According to the density of states analysis, the S-3p orbital for pristine ZrS2 monolayer and S-3p and Zr-4p orbitals for doped ZrS2 monolayers contribute to the VBM, but the Zr-3d orbital is contributed to the CBM. All the structures showed maximum optical conductivity and strong absorption with a maximum absorption coefficient over 104 cm−1 in the UV region, suggesting that the structure is very suitable for UV filter and detector applications.



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*Source: 6525507-2023-02-23.xml*