Effect of optoelectronic properties of vacancy defect in monolayer PtS 2 under strain: A first-principles study

doi:10.21203/rs.3.rs-5036304/v1

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Effect of optoelectronic properties of vacancy defect in monolayer PtS 2 under strain: A first-principles study

https://doi.org/10.21203/rs.3.rs-5036304/v1

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In this paper, the optoelectronic properties of monolayer PtS₂ under vacancy and strain are calculated based on density functional theory (DFT). Phonon spectrum verifies the stability of the model. Formation energy calculations show that the single S-atom defect system possesses lower energy and is easier to prepare experimentally. The single S-atom defect system is converted from an indirect bandgap to a direct bandgap, which is more favorable for electron transition. Under biaxial strain, the band gap of monolayer PtS₂ decreases with increasing tensile strain and increases with increasing compressive strain. In addition, optical property calculations show that the initial absorption and reflection coefficients of the defect system gradually increase under tensile strain and decrease under compressive strain, and are located in the low-energy region where red-shift and blue-shift phenomena occur respectively. This paper reveals the modulation effect of strain on the electronic properties of monolayer PtS₂ in the defect system, which is of great significance for the extension of material functionality and the optimization of device performance.

Monolayer PtS2

Optoelectronic properties

Defects

Strain

With the successful preparation of monolayer graphene in the laboratory, graphene has taken its place in the materials field due to its excellent electrical conductivity[1, 2]. However, graphene has zero bandgap electronic properties, and the lack of flexible control of its properties limits its role as an information transfer medium[3–5], such as integrated circuits or sensors. After the preparation of graphene induced a boom in nanomaterials research, similarly, single-layer transition metal sulfides (TMDCs) began to become a new type of material that people focused on[6–9]. Single-layer TMDCs have a three-layer structure when viewed from the side[10]. The upper and lower layers are made of S-atoms, and the middle layer is composed of transition metal atoms. Most of them are pentagonal materials. Unlike hexagonal materials, this kind of unique structure gives it unique and excellent electronic and optical properties and is expected to replace traditional bulk silicon materials and become the mainstream material in semiconductor manufacturing[11, 12].

Compared with materials such as MoS2 and PdS2, PtS2 has higher carrier mobility[13, 14]. Although the production cost of Pt is slightly higher than other materials, which limits its wide range of applications[15, 16]. However, because only a single layer is used in semiconductor nano-precision devices such as field-effect transistors (FETs) and diodes, the cost is greatly reduced, making single-layer PtS2 a candidate material in future semiconductor fields. We can modulate the electronic structure of monolayer TMDCs in various ways, such as by applying electric field, strain, doping, defects, adsorption, and then improving optoelectronic properties. It has been found that TMDCs materials are very likely to lose elements, especially S-atom, during the process of monolayer stripping or chemical vapor deposition (CVD), resulting in the formation of vacancy structures[17, 18]. Meanwhile, the defects can effectively trap free electrons as well as holes, resulting in electron localization and thus modulating the optoelectronic properties of the materials[19, 20]. Bao et al. demonstrated that S vacancies in TaS2 increase the overlap of electron clouds and charge aggregation and increase the electron transfer ability[21].Pan et al. investigated the N vacancy system of GaN and showed that the system is thermodynamically stable and improves the electron hopping ability[22].Ji et al. investigated the effect of applying different S defect concentrations to monolayer PtS2 on optoelectronic properties[11].

Flexible transformation of the bandgap can be realized by biaxial strain, which provides a very good prospect for the design of layered materials and contributes to the development of the field of optoelectronic devices[19, 20].Sohail et al. studied monolayer PtS2 and proved the feasibility of biaxial strain on the material conductivity, Seebeck coefficient, and power factor modulation[23].Guo et al. proved that applying biaxial compressive strains to PtSe2 can reduce the thermal conductivity of TMDCs and improve thermoelectric properties[24]; Liu et al. reduced the band gap by applying uniaxial, biaxial and shear strains to monolayer PtS2 and explored a significant red-shift in the spectrum with increasing strain[10]. Similarly, there are many studies on strain engineering.

However, the study of the optoelectronic properties of defect systems under strain has not been systematically reported yet. On the other hand, strain engineering is more easily realized than doping, adsorption, and other forms. Therefore, in this paper, we will explore the properties of PtS2 in terms of energy bands, density of states, optical absorption, and dielectric function by applying different biaxial directional strains in a single defect state, which will support the design and application of PtS2 in optoelectronic materials and also provide ideas for designing sensors and integrated circuits.

All properties based on density-functional theory (DFT) are performed using the CASTEP module under Materials Studio. The PBE generalization accurately describes the electronic structure and related properties of atoms and molecules by means of the GGA. The cut-off energy is set at 500 eV. The addition of a 20 Å vacuum layer effectively prevents periodic boundary effects. The energy bands, density of states, and optical properties are calculated using a 3 × 3 × 1 supercell. The sampling of the K-point grid in the Brillouin zone is set to 5 × 5 × 1. The energy band path is Γ-M-K-Γ and the BFGS model is used as the minimization algorithm in the calculation of single defect states. In order to have better convergence, the TPSD mode is chosen as the minimization algorithm when a biaxial directional strain is applied in the defect state. In addition, the phonon dispersion is calculated using the linear response theory.

3.1 Geometric structure

The Pt and S atoms of monolayer PtS2 are arranged in a two-dimensional plane in a cross-packed manner. As can be seen in Figs. 1(a,c), in the single-layer 3 × 3 × 1 supercell, the Pt-atoms are surrounded by S-atoms, each Pt-atom is bonded to six S-atoms, and the Pt-atoms in the middle layer are sandwiched between the S-atoms in the upper and lower layers, forming a kind of hexagonal structure. The Pt-atoms form bonds with the sulfur atoms in an octahedral geometry, and this arrangement gives PtS2 its unique properties. The optimized monolayer single-cell model is energy optimized with lattice parameters a = 3.59 Å, b = 3.59 Å, and the average bond length between Pt-atoms and S-atoms is 2.42 Å, which is basically in agreement with the computational and experimental data of previous studies[11, 12, 25]. Figure 1(b) represents the defect location as well as the stretching schematic. After the defect relaxation optimization of monolayer PtS2, the optimized geometrical parameters are listed in Table 1 in order to visualize the changes in the structural physical parameters. From Table 1, it can be seen that the defects lead to localized distortions in the atomic structure. The Pt-S bond closest to the defect shortens the distance between atoms, whether the structure is tensile or compressive in both directions. The lattice structure is again distorted by the external strain, leading to an increase in the bond length between atoms in the region away from the defect with increasing strain. It was also shown in subsequent energy band analyses that changes in these geometric structures will affect the intensity of interactions between atoms, thereby affecting their electronic structure and optical properties.

Table.1. Maximum and minimum bond lengths of monolayer PtS₂ with defects and different strain structures

Structure state	Pristine	Vs
Structure state	Pristine	-6%	-4%	-2%	0	2%	4%	6%
Min Bond (Å)	2.4183	2.3440	2.3357	2.3480	2.3657	2.3692	2.3949	2.3760
Max Bond (Å)	2.4185	2.4027	2.4325	2.4323	2.4323	2.4457	2.4578	2.4898

3.2 Stability

The structural stability of 2D materials is crucial in semiconductor preparation and practical applications. Considering firstly the phonon dispersion of the original structure of the monolayer[26], a total of nine phonon branches are demonstrated in Fig. 2, including three acoustic and six optical phonon branches, and it can be seen that there is no presence of imaginary frequencies, which indicates that the monolayer PtS₂ has a very stable nature.

Formation of the defective system was further calculated to verify the stability with the following equation:

$$\:{\text{E}}_{\text{form}}={\text{E}}_{\text{V}}^{\text{total}}-{\text{E}}_{\text{perfect}}+{\text{E}}_{\text{μ}}$$

where$\:\:{\text{E}}_{\text{form}}$ represents the formation energy, $\:{\text{E}}_{\text{V}}^{\text{total}}\:$represents the total energy after missing atoms, $\:{\text{E}}_{\text{perfect}}$ represents the total energy of the native structure, and $\:{\text{E}}_{\text{μ}}\:$represents the chemical potential of S-atom. The total energy of the native structure calculated based on density functional theory $\:{\text{E}}_{\text{form}}$=-11476.835 eV, the total energy with missing S-atom $\:{\text{E}}_{\text{Vs}}^{\text{total}}$=-11197.2 eV, the total energy with missing Pt-atom $\:{\text{E}}_{\text{Vpt}}^{\text{total}}$=-10754.934 eV, and the single S-atom energy $\:{\text{E}}_{\text{μ}}$= -273.856 eV, and single Pt-atom energy $\:{\text{E}}_{\text{μ}}$= -712.023 eV, resulting in formation energies of 5.779 and 9.878 under S and Pt vacancy respectively. In order to take into account the overall stability of the structure, the S vacancy(Vs) is selected as the object of the study, and the electronic as well as the optical properties of the structure are further regulated in the strain engineering below.

3.3 Electronic properties

Defects and biaxial strains are effective methods for modifying the properties of monolayer semiconductors. By using such methods, the energy band structure of the material can be changed. In this paper, the strain rate is defined as ε=(a-$\:{\text{a}}_{\text{0}}$)/ $\:{\text{a}}_{\text{0}}$, where a is the lattice constant after strain; $\:{\text{a}}_{\text{0}}$ is the pristine lattice constant. In Figs. 4 the energy band graphs of the pristine, defective, and externally strained structures of monolayer PtS2 are plotted. Figure 4(a) shows the energy band diagrams of the native structure; Fig. 4(b) shows the energy band diagrams in the Vs state; and Figs. 4(c-h) shows the biaxial strains applied in the defective state from − 6%~6%, respectively. The biaxial tensile strain is defined as positive; the biaxial compressive strain is defined as negative. The Fermi energy level for this study is defined at 0 eV.

The results of the study in Fig. 3 show that the top of the valence bands of these structures are close to the Fermi energy level. The lowest point of the conduction band CBM and the highest point of the valence band VBM of the monolayer PtS2 model calculated using the two generalizations are located at the Γ-M and K-Γ points in the Brillouin zone, respectively, and the GGA generalization presents an indirect bandgap of 1.774 eV, which is almost the same as that of the previous results[27–30]; whereas the HSE06 generalization presents an indirect bandgap of 2.941 eV. Although the band gap value under the GGA generalization is underestimated, the curvature of the energy band distribution of the two generalizations is basically the same, and the GGA generalization is used for all other calculations in this paper in consideration of the computational cost. According to previous studies on this material, the spin-orbit coupling (SOC) effect has only a small effect on the energy levels near the Fermi energy level of this material[12, 17], and the negligible SOC effect is not considered here.

After the introduction of the S defect, the conduction and valence bands are shifted downward in general, the natural band gap increases to 1.844 eV, and three defect bands are formed in the forbidden band. This is due to the fact that the removal of S breaks all three Pt-S bonds and enriches two electrons in the supercell system, forming new energy levels. The appearance of the defect bands reduces the bandwidth to 0.585 eV, which becomes a direct bandgap, allowing electrons to jump from the valence band to the defect bands first and then to the conduction band, which makes it easier for electrons to excite the transition and increases the conductivity of the material.

The electronic properties of the material are then controlled by biaxial extension and compressive of the structure. As shown in Figs. 4(c-h), we can see that the strain has a controlled modulation of the energy bands and the defect bands are still evident. With the increase of biaxial tensile strain, the overall shift of the conduction band to the low-energy region. The energy band decreases from 0.585 eV to 0.192 eV; However, with the increase of biaxial negative strain, the valence band as a whole moves to the high-energy region, and the energy band increases to 0.837 eV. As shown in Fig. 5, the compressive strain energy band changes more smoothly and slowly than the tensile strain energy band. Compared with the pristine structure, the S defects and the stacking degree of the model after strain increase, the degeneracy becomes stronger, the conduction and valence bands become smoother in energy level, the effective mass of the electrons increases, the conductivity decreases, and the response speed becomes weaker.

Analyzing the total density of states (DOS) and the partial density of states (PDOS) is also a way to understand the electronic structure of a material. The DOS helps to understand the overall distribution information of electronic states, while the PDOS helps to understand the contribution of different atoms or orbitals to the electronic structure. As shown in Fig. 6(a), The energy levels between − 14.4 and − 11.7 eV are mainly contributed by the S-3p orbitals, with minor contributions from the Pt-6s and Pt-5d orbitals, resulting in relatively unstable covalent bonds. In the range of -6.5 to 0 eV, the Pt-5d and S-3p orbitals dominate, playing a crucial role in determining the valence band position near the Fermi level. Localized hybridization occurs between these atomic orbitals, forming stronger covalent bonds. The range of 1.77 to 3.6 eV is primarily influenced by the Pt-5d and S-3p orbitals, jointly contributing to the lowest point of the conduction band in the band structure. In the range of 5.1 to 10 eV, the Pt-5d and S-3p orbitals also play a significant role. As shown in Fig. 6(b), introducing Vs leads to the appearance of several small peaks. The peak values near − 13.2 eV, -4.9 eV, -3.9 eV, and − 0.6 eV in the valence band decrease overall, indicating a reduction in the number of electrons at these energy levels. Additionally, the valence band shifts toward lower energy. Three new small peaks form in the ranges of -0.5 to 0 eV and 0.5 to 1.5 eV, resulting from the hybridization of Pt-5d and S-3p orbitals, creating new defect levels and reducing the band gap.

In order to better explore whether applying strain to new semiconductor materials in the presence of defects will lose their electronic properties, the density of states under strain was also summarized. The energy levels near the Fermi level best reflect the electronic properties of the material, so in strain engineering, the energy range of the density of states diagram is only considered to be -6 ~ 4 eV. As shown in Fig. 7, as the biaxial tensile strain increases in the defect structure, the overall conduction band gradually approaches the Fermi level, which directly reflects the decrease in the band gap, and the density of states curve becomes smoother. It is worth noting that at 0.6 eV and 4% tensile strain near 1.5 eV, there is stronger electron localization. However, in the valence band part, as the biaxial tensile strain increases, the peak value becomes smaller and the electron localization ability is weak. Similarly, as the biaxial compressive strain increases, the conduction band moves to the high energy region as a whole, and the band gap increases; the electron localization in the valence band also becomes lower.

3.4 Optical properties

The performance of optoelectronic devices is highly dependent on the optical properties of the material. By systematically measuring and analyzing the optical properties of a material, its absorption and emission efficiencies in different energy ranges can be evaluated, and thus its suitability for specific optoelectronic applications can be judged. The dielectric function connects the optical properties and electronic structure of a material by revealing the jumping behavior of electrons in the material. This makes it a key tool in the study of the physical properties of materials, helping us to understand and predict their behavior and application potential under different conditions. The Kramers-Kronig dispersion relation allows for the calculation of the dielectric function of optical properties with the following expression:

$$\:\epsilon\:\left(\omega\:\right)={\text{ε}}_{\text{1}}\:\left(\omega\:\right)\:+\:i{\text{ε}}_{\text{2}}\:\left(\omega\:\right)$$

where $\:{\text{ε}}_{\text{1}}$ (ω), i$\:{\text{ε}}_{\text{2}}$ (ω) denote the real and imaginary parts of the dielectric function, respectively. It can be seen from Fig. 8(a) that the static dielectric constant is almost negatively correlated with the band gap. After introducing defects, the static dielectric constant increases from 4.7 to 7.9; in the case of introducing defects and strain, the static dielectric constant increases significantly compared with the original PtS2 structure, especially at 4% strain defect reaches the maximum value under the condition, but the difference is small under the biaxial tensile strain of 6% and 4%; the static dielectric constant increases with the increase of tensile strain, similarly, decreases with the increase of compressive strain. Therefore, it can be concluded that the polarization ability of the high tensile strain defect structure will be significantly improved, the charge binding ability is strong, the carrier mobility ability is improved, and the conductive properties of the material are affected. At around 3 eV, the application of biaxial tensile strain causes a red-shift, which means that the band gap narrows. At the same position, the application of biaxial compressive strain causes a blue-shift and the band gap becomes wider. The imaginary part of the dielectric function is also called the loss factor. The greater the conductivity, the greater the imaginary part of the loss, which is related to the electron mobility and spectral response range. Figure 8(b) shows that the original structure forms a maximum virtual peak of 5.4 at 2.5 eV, and the maximum peak decreases to 4.6 after introducing defects. Under biaxial tensile strain, a new virtual peak is formed near 0.4 eV, and the conductivity is strong in this energy range, and the corresponding loss is also large; Peaks at 2.5 eV and 7 eV are second only to those of the pristine structure, indicating that the transformed structure has less loss than the pristine structure. The density of states can be used to explain the transition from S-3p to Pt-5d. After applying compressive strain, the peak value gradually decreases and blue-shifts. The tensile strain is red-shifted, the spectral response range of the material increases, and the photoinduced electronic transition is enhanced.

Similarly, the properties of absorption and reflection of visible light are critical for materials. Absorption describes the attenuation of light intensity per unit distance[31]; the reflectance spectrum is the variation of reflectance with wavelength[32–34]. As shown in Figs. 8(c,d), the absorption peaks of the original model appear at 3.4 eV,7.4 eV and 12.7 eV, respectively, and all of them are located in the UV region, indicating it has a strong UV absorption ability. While the first reflection peak appears in the visible region, the rest of the peaks are located in the UV region. This indicates that the material is highly reflective of both visible and UV light. After the introduction of the defect, the energy positions of the three peaks remain almost the same, but the absorption and reflection peaks are reduced. Under biaxial strain in the defect structure, tensile strain leads to a significant increase in the initial absorption and reflection coefficients compared to the pristine single-defect state, and the absorption spectrum is red-shifted at 3.4 eV with an increase in the visible response, but there is little change in the reflection spectrum. Compressive strains result in a significant decrease in the initial absorption and reflection coefficients, a blue-shift at the same location as described above, and a corresponding increase in the UV. The compressive strain of 6% at 13 eV, located in the high energy region, is greater than the absorption and reflection coefficients of pristine PtS₂ and is blue-shifted, with an increase in the transmittance of the material.

In this article, density functional theory (DFT) is used to calculate the optical properties such as the formation energy, phonon dispersion, energy band, density of states, and complex dielectric function of a single layer of PtS2. The results show that in the energy band diagram of the defect structure, defect bands will appear in the forbidden band, forming a narrow band gap. The band gap changes monotonically with increasing biaxial tensile and compressive strains. Under biaxial strain, the static dielectric constant increases significantly, the polarization ability is improved, and the charge-binding ability is strong. Under biaxial tensile strain defects, the initial absorption and reflection coefficients gradually increase compared with the single defect structure and are red-shifted in the near-ultraviolet region, and visible light increases accordingly. The defect structure of biaxial compressive strain is contrary to the above conclusion. The near-ultraviolet region undergoes a blue shift, which increases the performance in the ultraviolet region. It is worth mentioning that under the 4% strain defect structure, the static dielectric function is the largest, the polarization ability is the largest, and the current formed in the low energy region is also larger. Located in the high-energy photon region, the − 6% biaxial compressive strain is greater than the UV light absorption and reflection coefficient of the original PtS2, providing a theoretical basis for the development of new dielectric materials.

Funding

National Natural Science Foundation of China (Approval No: 11102118);

Liaoning Province “Millions of Talents Project” Fund (Approval No: 100010131)

Competing Interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability

The datasets generated during and analyzed during the current study are available from the corresponding author on reasonable request.

Author Contributions

Hang Yang: Writing-review&editing, Writing-original draft, Methodology, Conceptualization. Lu Yang: Data curation and Supervision. Jinlin Bao: Validation. Huaidong Liu：Discussion. Yanshen Zhao：Data curation.

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Effect of optoelectronic properties of vacancy defect in monolayer PtS 2 under strain: A first-principles study

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1. Introduction

2. Calculation method

3. Results

3.1 Geometric structure

3.2 Stability

3.3 Electronic properties

3.4 Optical properties

Conclusion

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References

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