Tuning electronic and optical properties of monolayer PdSe2 by introducing defects: first-principles calculations

Based on the density functional theory, the electronic and optical properties of pristine monolayer PdSe2 with Pd or Se vacancy-defect are investigated. Our results show that the Se defect is energetically more favorable than that of Pd defect. The band gap reduces, and some new midgap states appear after the Pd or Se defects are introduced. In terms of the optical properties, the prominent anisotropic characters are remained. The obvious new peaks of the dielectric constant appear after introducing defects. The light absorption in the visible energy range expands based on the appearance of the midgap states induced by the Pd or Se defects. The changes of the refractive index and reflectivity are similar with those of the dielectric constants and the light absorption. The energy loss spectrum of the PdSe2 with Pd or Se defects is obviously different, which can be used to identify different defects in PdSe2. These findings provide effective strategies to tune electronic and optical properties of monolayer PdSe2 by introducing defects.

existence of the point defects in semiconductors can efficiently trap free electrons, holes and localize excitons. When it recombines radiatively, the excitons can lead to light emission at energies lower than the band-to-band optical transition energy. On account of tighter localization of the electron wavefunction, the interactions between the defects and excitons become stronger in reduced dimensionalities materials 29 . On one hand, for monolayer PdSe 2 , it is highly desirable to explore the optical and electronic properties and develop simple and effective strategies to improve them. This will not only help to enhance the performance of device dependent on monolayer PdSe 2 but also contribute to its applications in nanoelectronic devices. On the other hand, Lin et al. have reported that they have synthesized a novel 2D material monolayer Pd 2 Se 3 , which is a fusion of two defective PdSe 2 layers due to the Se vacancies with a certain concentration 30,31 . They have systematically stated that the monolayer Pd 2 Se 3 has excellent anisotropic electronic and optical properties and is a very promising candidate for photovoltaics. Take these things into account, we can infer that it is valuable to investigate the effects of the defects on the electronic and optical properties of PdSe 2 . In this work, we perform the first-principles calculations to investigate the electronic and optical properties of monolayer PdSe 2 with Pd or Se vacancy defects, the Pd or Se defects are introduced by the random elimination of atoms. After introducing defects, obvious changes for electronic and optical properties of PdSe 2 can be obtained.

Results and Discussions
Firstly, the structural parameters of PdSe 2 monolayer, PdSe 2 with Pd or Se defects are calculated. The bond lengths and angles of vacancy-defected PdSe 2 have little changes compared with the primitive cell, which means that there is only a slight distortion of the system, so the PdSe 2 with a Pd or Se defect is stable. In order to further compare these two defects, the formation energies are obtained through the following equation , where E defect represents total energies of the relaxed PdSe 2 with Pd or Se defect, E pristine is the energy of the pristine PdSe 2 , μ n is the chemical potential of the Pd or Se atom defect. The more positive the E form is, the more difficult the defect to be formed. From our calculations, it can be obtained that the E form of PdSe 2 with Se defect is 1.38 eV, while for the PdSe 2 with Pd defect, it is 1.97 eV, so Se defect is the more energetically favorable type. Recent work also has experimentally demonstrated the presence of Se defect in PdSe 2 32 . To further clarify the effects of defect on the electronic properties of monolayer PdSe 2 , the band structures along high symmetry k-points are depicted in Fig. 1. Figure 1(a-c) represent the band structures with PBE, Fig. 1(d-f) represent the band structures based on HSE06, respectively. By contrast, it can be found that the PBE underestimates the band gap, the HSE06 is more reasonable to calculate the electronic and optical properties, so the HSE06 are adopted in all the following calculations. As shown in Fig. 1(d), the pristine structure of monolayer PdSe 2 has an indirect band gap about 2.25 eV, which is consistent with previous work 33 . However, after introducing Pd or Se defects, the band gaps are 1.45 and 1.91 eV, respectively. It can be observed from Fig. 1(e,f) that the presence of Pd or Se defect leads to some different new midgap states within the energy band gap, which can also be identified by the sharp peaks in the density of states. All the systems remain indirect band gap, and the PdSe 2 with Pd defect still shows semiconductor characteristics. For the PdSe 2 with Se defect, the band of midgap state goes through the Fermi level, the PdSe 2 shows metal characteristics. It is also indicated that introducing defects is a potentially useful strategy to tune the band gap of 2D materials.
The total density of states (TDOS) and projected density of states (PDOS) for pristine PdSe 2 , PdSe 2 with Pd or Se defect are shown in Fig. 2. For pristine PdSe 2 , it can be found that the dx 2 , dxy orbital of Pd atoms and the px, pz orbital of Se atoms mainly contribute to the states at conduction band edge, the dz 2 orbital of Pd atoms and the px, pz orbital of Se atoms mainly contribute to the valence band edge. Besides, there is significant hybridization between Pd d and Se p states. While after introducing the defects, there are some changes, as shown in Fig. 2(b,c). It is obvious that the midgap states are mainly originated from the p x and pz orbital of Se atoms in PdSe 2 with Pd defect, while for PdSe 2 with Se defect, the midgap states mainly originate from dx 2 and dxy orbital. In general, the appearance of the peaks in the gapped region of the DOS are associated with the midgap states localized around the defects, which arises from the dangling bonds of Pd or Se due to their unsaturated charges, and their strength depends on the different missing atoms 34 . Thus one can identify the types of defect through the PDOS and then characterize the PdSe 2 in order to get expected electronic properties.
Optical properties of the materials are closely connected to its electronic properties. And it is evident from the previous calculations that the defects can alter the electronic properties of monolayer PdSe 2 , the change of electronic properties is expected to modify the optical properties. Figure 3(a-c) represent the real parts of the dielectric constant ε 1 for pristine PdSe 2, PdSe 2 with Pd or Se defect, (d)-(f) represent the corresponding imaginary parts ε 2 , respectively. From Fig. 3(a-c), it can be found that the maximum value of ε 1 in x direction for pristine PdSe 2 is about 7.62, however, it reduces to 6.94 and 4.15 for PdSe 2 with Pd or Se defect, respectively. The maximum values are 7.06, 6.41 and 4.02 for pristine PdSe 2 , PdSe 2 with Pd or Se defect in y direction of ε 1 , which is different from those in x direction. After introducing defect, the maximum value of ε 2 also decreases from 6.03 for pristine PdSe 2 to 5.39 and 3.36 for PdSe 2 with Pd or Se defect in x direction, respectively. It can be found that the change of ε 2 is different as well both in x and y directions, which means that the anisotropy of the optical properties of PdSe 2 remains unchanged. Furthermore, the peaks in the low energy range of dielectric constant correspond to the peaks in the DOS, which mainly due to the new midgap states originated from the defects.
The absorption coefficients α(ω) for pristine PdSe 2 , PdSe 2 with Pd or Se defect have been depicted to reveal the light absorption properties of PdSe 2 , which are shown in Fig. 4. The optical absorption spectrum is closely related to the imaginary parts of the dielectric constant. It can be observed that there is no absorption within the energy range of 0 to 2.20 eV for pristine PdSe 2 as shown in Fig. 4(a), which is consistent with the band gap structure in Fig. 1(d). According to the suitable band gap, monolayer PdSe 2 is expected to be a promising candidate for light absorption. Monolayer PdSe 2 exhibits good optical absorption in the visible regions (1.64-3.19 eV) as is shown in Fig. 4(a). After introducing the Pd or Se defect, the absorption is optimized obviously. The optical absorption starts from 0.44 and 0.53 eV for the PdSe 2 with Pd or Se defect, which are shown in Fig. 4(b,c). That is to say, the www.nature.com/scientificreports www.nature.com/scientificreports/ optical absorption in low energy region widens, especially in the visible regions. That is benefit from the existence of the Pd or Se defect in PdSe 2 , they can create some midgap states, so more new optical transitions can be activated comparing with the case of pristine PdSe 2 . In addition, it can be found that the absorption coefficients are different in x and y directions. Figure 5 shows the refractive index n(ω) and reflectivity R(ω) of PdSe 2 systems. The maximum value of n(ω) for pristine PdSe 2 is about 2.82. There is noticeable change for the maximum n(ω) of the PdSe 2 with Pd or Se defect compared with that of pristine PdSe 2 , it decreases to 2.72 and 2.01. And the new peak of n(ω) appears in low energy region obviously as shown in Fig. 5(b,c), which is consistent with the dielectric constant. The R(ω) of PdSe 2 systems are shown in Fig. 5(d-f) respectively. The maximum R(ω) for the pristine PdSe 2 and PdSe 2 with Pd or Se defects are 0.32, 0.25 and 0.17, respectively. It is obvious that the maximum R(ω) decreases compared with that in pristine PdSe 2 , and there are new peaks in low energy region after introducing Pd and Se defects. All the new peaks in low energy region are related to the new midgap states.
The electron energy loss spectrum L(ω) have also been depicted for pristine PdSe 2 , PdSe 2 with Pd or Se defect, which are shown in Fig. 6(a-c), respectively. By contrast, it can be found that obvious differences occurred due to the introduction of the defects. The L(ω) starts from 2.31, 0.31 and 0.45 eV for pristine PdSe 2 , PdSe 2 with Pd or Se defect, respectively. The first sharp peak of L(ω) is observed at 5.13, 1.75 and 0.68 eV. Besides, the curves of pristine PdSe 2 and PdSe 2 with Se defect have a tendency of ascending first and descending in succession then www.nature.com/scientificreports www.nature.com/scientificreports/ ascending. While the curve of PdSe 2 with Pd defect has a tendency of ascending first and descending in succession, and it has relatively dense peaks. The different L(ω) can be used to identify different defects.

conclusions
In this work, the electronic and optical properties of pristine PdSe 2 , PdSe 2 with Pd or Se defect are studied through the first-principles calculations based on the density functional theory. The result of the formation energies indicates that Se defect is more energetically favorable compared with that of Pd defect. By calculating the band structures, it is found that the band gap reduces due to the appearing of the new midgap states after introducing Pd or    www.nature.com/scientificreports www.nature.com/scientificreports/ Se defect. The midgap states are originated from the dangling bonds of Pd or Se due to their unsaturated charges. In terms of the optical properties, the dielectric constant and absorption spectrum, refractive index, reflectivity and electron energy loss spectrum have been analyzed. The obvious peaks of the dielectric constant and the absorption spectrum in low energy region can be observed due to the appearance of the new midgap states induced by the Pd or Se defect. And the prominent anisotropic characters are remained. The light absorption area in the visible regions widens after introducing Pd or Se defect compared with that of pristine PdSe 2 . The new peaks benefit from the appearance of the midgap states which activate more new optical transitions in the optical spectrum. For the refractive index and reflectivity, the similar changes have been taken place. Furthermore, the difference of the electron energy loss spectrum can be used to identify different defects. All these findings provide effective strategies to tune electronic and optical properties of monolayer PdSe 2 , and provide possibilities for monolayer PdSe 2 in the applications of optoelectronics. theoretical model and computational details. All our theoretical calculations are performed through VASP (Vienna ab-initio Simulation Package) 35,36 , PAW pseudopotential is used to describe the interaction between ions and electrons 37,38 . In terms of the energy exchange correlation energy function, the generalized gradient approximation (GGA) in the form of Perdew-Burke-Ernzerhof (PBE) is used 39 . The electronics and optical properties are calculated by the hybrid functional based on the Heyd-Scuseria-Ernzerhof (HSE06) exchange-correlation functional 40 . The cut-off energy is 400 eV in the process of the structural optimizations and calculations. The 11 × 11 × 1 Monkhorst-Pack grid is chosen when calculating the integral in Brillouin zone. Energy convergence is set to less than 10 −4 eV and the convergence accuracy of the nuclear motion is set to less than 0.01 eV/Å. A 3 × 3 × 1 supercell (54 atoms) of PdSe 2 is constructed, as shown in Fig. 7. It is worth noting that the residual strain may exist due to the limit of periodic boundary condition no matter how bigger the supercell is. In order to avoid the interlayer interference, the thickness of the vacuum layer is set to 20 Å.
The optical properties are general evaluated by the dielectric function which are the sum of real and imaginary parts, ε ω ε ω ε ω = +i ( ) ( ) ( ) 1 2 . The imaginary part is calculated by the summation of empty band states using the following equation 41 , www.nature.com/scientificreports www.nature.com/scientificreports/ where Ω represents the volume, v and c correspond to the valence and the conduction band respectively, α and β indicate the Cartesian components, e α and e β are the unit vectors, ck ∈ and vk ∈ refer to the energy of conduction and valence band respectively, u ck is the cell periodic part of the orbitals at the k-point. The real part of dielectric constant is calculated by the Kramers-Kronig relation 42 1 0 with P being the principle value. According to the values of real and imaginary part of the dielectric constant, the optical absorption coefficient α(ω), the refractive index n(ω), the reflectivity R(ω), and the electron energy loss spectroscopy L(ω) can be given by 43 ,