Introduction

Two-dimensional (2D) transition-metal dichalcogenides (TMDs) represent a new family of 2D materials beyond graphene. They have a general formula of MX2 where M is a transition metal from group 4–10 and X is a chalcogen (S, Se, or Te). In contrast to graphene and their bulk materials, some 2D-TMDs are semiconducting with a sizable band gap, partially due to quantum-confinement effects. So far, theoretical and experimental efforts have been mainly focused on semiconducting 2D-TMDs with M = Mo and W1,2,3,4, due to potential applications in terahertz switch5, lasers and LEDs6, ambipolar ionic liquid gated field-effect transistor7, photo detectors1, and so on8. In a recent work9, PtSe2 monolayer was synthesized via a single step of direct selenization of a Pt(111) substrate and demonstrated to have potential application as valleytronics and photocatalyst.

Beside platinum, palladium (Pd) can also form binary compounds with Se with different stoichiometries and crystal structures, such as trigonal α-Pd4Se, tetragonal PdSe, cubic Pd17Se15, monoclinic Pd7Se2, and orthorhombic PdSe210. Under ambient conditions, PdSe2 crystal appears in an orthorhombic structure with a space group of Pbca similar to the case of PdS211,12. Using first-principles calculations, Sun et al., proposed a PdSe2 monolayer with semiconducting nature and high Seebeck coefficients11. So far, PdSe2 monolayer has not been achieved experimentally, partially due to the strong layer binding energy ~190 meV/atom in orthorhombic PdSe2 bulk crystal which makes the exfoliation of PdSe2 monolayer difficult. However, the recently success in the synthesis of PtSe2 monolayer on Pt(111) substrate via selenization opens an avenue towards this goal.

In this manuscript, we proposed a novel stable configuration of PdSe2 monolayer that can be synthesized by selenizing Pd(111) surface, as shown in Fig. 1(a). Our first-principles calculations indicate that it is energetically comparable to the Pbca phase11. Phonon spectrum analysis confirms its dynamics stability. This PdSe2 monolayer has an indirect-band-gap of about 1.10 eV, suitable for application in infrared light region. It also has high electron mobility of about 9800–42000 cm2v−1s−1 which is larger than that in monolayer black phosphorus by more than one order. The in-plane stiffness of 54 J/m2 is only half of MoS2, allowing a large tensile strain up to 35%. Additionally, tensile strain can significantly reduce the band gap and consequently enhance the infrared light adsorption ability. These interesting properties are quite promising for application in electronic and optoelectronic devices.

Figure 1
figure 1

(a) The top view and side view of atomic configuration for PdSe2 monolayer on Pd(111) surface. The blue and cyan balls are Pd atoms and gray ball are Se atoms. The small and large black parallelograms represent primitive lattice for monolayer PdSe2 and PdSe2-Pd(111) superstructure, respectively. The black arrows indicate the x- and y-direction for top view. (b) The phonon spectrum of PdSe2 monolayer. (c) Three-dimensional plot of strain energy ES (see text) depending on strain of εx and εy(see text). The color filled contour of the fitted formula is also plotted. (d) The energy evolution of PdSe2 monolayer under biaxial compressive and tensile strains. The energy at the equilibrium state was set to zero.

Full size image

Results and Discussion

Atomic structure and stability

The atomic structure of a freestanding PdSe2 monolayer with a P-3M1 space group is similar with that of PdSe2 monolayer grown on the Pd(111) surface, as shown in Fig. 1(a). Each Pd atom bonds to six Se atoms and each Se atom is coordinated by three Pd atoms. All the Pd atoms are on a same plane sandwiched by two Se planes. The thickness of the freestanding PdSe2 monolayer measured from the distance between the two Se planes is 2.631 Å. The Pd-Se bond length is about 2.528 Å. The optimized lattice constant of the hexagonal lattice is 3.739 Å, quite close to that of the PtSe2 monolayer, 3.7 Å 9. Notably, a 3 × 3 PdSe2 monolayer (11.217 Å) matches well with the 4 × 4 Pd(111) surface (11.186 Å), which implies high plausibility of growing PdSe2 monolayer on Pd(111) surface via selenization. This allows us to build a PdSe2/Pd heterostructure by placing a 3 × 3 PdSe2 on Pd(111) surface without considering the small lattice mismatch (~0.3%). Compared with freestanding monolayer, the buckling of the supported PdSe2 increases to 2.710 Å and the bond length vary from 2.51 Å to 2.61 Å with an average of 2.55 Å, due to the substrate effect. The distance between PdSe2 monolayer and substrate is about 2.16 Å, and the binding energy between them is −1.04 eV per PdSe2 unit. The PdSe2-Pd(111) interaction is much stronger than the van der Waals (VDW) interaction in graphite (~−36 meV/atom), making the exfoliation of PdSe2 from the Pd substrate difficult.

It is noteworthy that the lattice structure of hexagonal PtSe2 monolayer differs significantly from that cut from orthorhombic PdSe2 crystal11. The latter case has orthorhombic symmetry with four-coordinated Pt atoms and two-coordinated Se atoms, and is slightly stable than the hexagonal structure by about 26 meV/atom. However, the hexagonal PdSe2 monolayer matches well with the Pd(111) surface in both symmetry and lattice constant along with a negative binding energy (−1.04 eV per PdSe2 unit) and thus has high plausibility on the Pd(111) surface as the surface is selenized9.

To confirm the dynamic stability of the PdSe2 monolayer, we calculated the phonon spectrum using a finite displacement method implemented the Phonopy code interfaced the VASP code13,14. It was found that the phonon spectrum is free from imaginary frequency modes, as shown in Fig. 1(b), suggesting the dynamic stability of the PdSe2 monolayer. Additionally, there is a small energy gap between the acoustic and optical branches in the phonon spectrum. Such an energy gap can protect the vibration of acoustic modes from being interrupted by optical phonon15,16,17, which leads to the resonators with higher quality factor than the graphene resonators18.

Mechanical properties

Strain is not evitable as a monolayer is grown on a substrate. We therefore investigated the mechanical properties PdSe2 monolayer from first-principles. To obtain the elastic modulus in harmonic range, we employed a rectangular supercell and applied strains along x- and y-direction, as shown in Fig. 1(a). The energy (Es) dependence of strains is illustrated in Fig. 1(c). The data is fitted to a two-dimensional polynomial expressed by , where εx and εy represent the strains applied along x- and y-direction, respectively. The total energy of system at the equilibrium state was set to zero. It was found that the two parameters a1 and a2 are almost identical due to the isotropy in the honeycomb symmetry19. The poisson’s ratio (ν) and in-plane stiffness (C) can be obtained as and 20, where A0 is the equilibrium area of the structure. The calculated poisson’s ratio (0.29) is close to those of MoS2 (0.25) and silicene (0.30) but larger than that of graphene (0.16). The in-plane stiffness of PdSe2 monolayer, 54 J/m2, is much smaller than those of MoS2 (123 J/m2) and graphene (335 J/m2)19,21, suggesting that PdSe2 monolayer is softer than both graphene and MoS2 monolayer.

The softness of PdSe2 monolayer was also confirmed by the energetic and structural evolution as a function of biaxial strain. Figure 1(d) gives the energy increase of PdSe2 monolayer as the biaxial strain varies from −9% (compression) up to 35%. It is interesting to see that energy varies continuously without abrupt decrease, indicating that no Pd-Se bonds are broken in this region. As the tensile strain exceeds 35%, energy decreases drastically and irreversible structure modification along with Pd-Se bond breakage takes place. The two energy local minima at ε = 0 and 20.4% correspond to the equilibrium state and a metal-stable state of PdSe2 monolayer. The later configuration has the Pd-Se bond length of 2.639 Å, slightly longer than that of the equilibrium state by about 4.4%, but the thickness is greatly reduced to 0.918 Å compared to the equilibrium state value 2.631 Å. The metastable state represents a low-buckled configuration of PdSe2 monolayer under high tensile strain. Similar results have also been reported for silicene, but the critical tensile strain in PdSe2 monolayer is much larger than that in silicene21.

Electronic properties

We then calculated the electronic structure of PdSe2 monolayer from first-principles. We employed the PBE functional and Heyd–Scuseria–Ernzerhof (HSE) screened Coulomb hybrid density functional22 in the framework of DFT. The band structure and electronic density of states (DOS) near the Fermi level are illustrated in Fig. 2(a). Both functionals gave the semiconducting nature of PdSe2 monolayer with an indirect band gap, similar to the case of orthorhombic PdSe211. The valence band maximum (VBM) resides at the Г (0, 0, 0) point while the conduction band minimum (CBM) locates in between Г (0, 0, 0) and M (0.5, 0, 0). Six valleys are therefore found in the whole Brillouin zone as shown in Fig. 2(b), which gives opportunities to valley devices. The PBE functional underestimated the band gap value (0.7 eV) compared with HSE functional (1.10 eV). The band gap of PdSe2 monolayer is slightly smaller than that of PtSe2 monolayer (1.2 eV)9 and orthorhombic PdSe2(1.43 eV)11 and suitable for adsorbing infrared light. From the orbital-resolved electron density of states shown in Fig. 2(a), we can see that the VBM is mainly contributed by the 4p orbits of Se atoms, while the CBM comes mainly from the 4d orbits of Pd and 4p orbits of Se. This is consistent with the features of the Kohn-Sham wavefunctions of the VBM and CBM plotted in Fig. 2(d). Considering Pd is a heave element, we also took the spin-orbit coupling (SOC) effect into account in electronic structure calculations. It was found that the energy degeneracy at some highly-symmetric points in BZ is lifted due to SOC (Fig. S2 in Supplementary Information). Both the valence and conduction bands are shifted downward and the global indirect band gap is decreased by about 0.2 eV. The reduced band gap would lead to red shift of optical adsorption peaks and thus facilitate the adsorption of infrared light.

Figure 2
figure 2

(a) Bands structures of PdSe2 monolayer along the high symmetric points in the BZ (right) and orbital-resolved electron density of states (left). The energy at the Fermi level is set to zero. The black lines and purple lines represent the data obtained from HSE and PBE functionals, respectively. M (1/2, 0, 0), G (0, 0, 0) and K (1/3, 1/3, 0) represent high symmetric points in the reciprocal space. The momentum-dependent energy distribution in BZ for (b) the lowest unoccupied band and (c) the highest occupied band. (d) Electron density profiles of the Kohn-Sham wavefunctions for CBM and VBM.

Full size image

When PdSe2 monolayer is grown on Pd(111) substrate, the energy bands of semiconducting PdSe2 and metallic Pd substrate mix together. Slight electron redistribution takes place in PdSe2 monolayer. About 0.05 electrons per Se atom transfer from upper Se layer to down Se layer, while the electron transfer from PdSe2 monolayer to substrate is almost negligible (~0.007 |e| per PdSe2 unit). This slightly reduces the workfunction of PdSe2 to 5.20 eV compared with that of freestanding PdSe2 monolayer (5.40 eV). We also calculated the electronic structures of PdSe2 multilayers built by stacking PdSe2 monolayers with different patterns. For the PdSe2 bilayer, AA stacking pattern is energetically more favorable than AB pattern (Supplementary Information). The interlayer interaction greatly reduces the band gap of 2D PdSe2. The band gap of the PdSe2 bilayer with AB pattern is only 0.33 eV (PBE), while the energetically preferred AA pattern becomes metallic.

We also calculated the electron mobility of PdSe2 monolayer using the phonon-limited scattering model23,24. In the method, the electron mobility can be evaluated using the expression24,25,26, ; where e is the electron charge, ℏ is Planck’s constant divided by 2π, kB is Boltzmann’s constant and T is the temperature. me is effective mass of electron in the transport direction (either mx or my along the x and y direction, respectively) and ma is the averaged effective mass of that along x and y direction determined by . Deformation potential constant of CBM (El) for electrons along the transport direction is defined by , ΔV is the energy change of CBM, l0 is the lattice constant in the transport direction and Δl is the change of l0. The elastic modulus C2D of the longitudinal strain in the propagation directions of the longitudinal acoustic wave is derived from ; where E is the total energy and S0 is the lattice area at equilibrium for 2D system. The electron mobilities along x- and y-direction are 9800 cm2v−1s−1 and 42000 cm2v−1s−1 at 300 K, respectively. These values are much higher than that in monolayer black phosphorus by more than one order of magnitudes. Such high electron mobility is quite promising for improving the photocatalytic activity of PdSe2 monolayer, because the photo-generated electrons can be easily transferred9.

The electronic structure modification of PdSe2 monolayer in response to tensile strain was then investigated. With the increase of tensile strain, the band gap of PdSe2 monolayer decreases and comes to close as the tensile is larger than 14%. More interestingly, compressive strain also reduces the band gap of PdSe2 monolayer. To reveal the origins of the strain-induced band gap modulation, we plotted the band structures of PdSe2 monolayer under difference strains in Fig. 3(a). From this figure, we can see that under a tensile strain, the CBM move downwards while the VBM varies slightly, reducing the band gap. This may be related to the enhancement of the Se_4p and Pd_4d interaction due to the shorten distance between the Se plane and Pd plane. Under a compressive strain, however, the VBM is sensitive to strain and shifts upwards, leading to band gap reduction. Besides, it is interesting to see that tensile strain decreases the energy of the G points (illustrated by green arrow in Fig. 3(a)), and lifts the energies of the N and N’ points (illustrated by red arrow in Fig. 3(a)). As the tensile strain is larger than 4%, the energy difference between the N and N’ points becomes very small, making the PdSe2 a quasi-direct band semiconductor.

Figure 3
figure 3

(a) The electronic band structures of PdSe2 monolayer under different strains obtained from PBE functional. The vacuum level is set to 0 eV. The regions of valence bands are covered by translucent blue. (b) Strain-dependent absorption coefficient of PdSe2 monolayer calculated by using HSE functional. The insert number donates the biaxial strain.

Full size image

Optical adsorption

The strain-induced band gap reduction affects the optoelectronic properties of PdSe2 monolayer. We calculated the imaginary part of complex dielectric function using the expression:

The indices c and v refer to conduction and valence band states respectively. uc k is the cell periodic part of the orbitals at the k-point k. ω is the frequency of the incident photon. The real part of the dielectric function is obtained from the imaginary part with the Kramers-Kroning relations. The optical absorption coefficient is given by ; where and is the real and imaginary part of complex dielectric function. The optical absorption coefficient I(ω) calculated using HSE functional is plotted in Fig. 3(b). At equilibrium state, the adsorption peaks locate in the visible light and ultraviolet light region. A small compression has little affect on the adsorption properties. When a tensile strain is applied to PdSe2 monolayer, adsorption peaks come to appear in the low energy region, due to the band gap reduction. Meanwhile, the adsorption to visible light is partially screened. For example, under the tensile strains larger than 12%, the adsorption coefficients are almost zero in the energy region from 1.0–2.0 eV. These fascinating properties are quite promising for infrared detectors where the screening of visible light adsorption is needed.

Conclusion

In summary, based on first-principles calculations, we proposed a stable form of palladium diselenide (PdSe2) monolayer that may be synthesized by selenizing Pd(111) surface. The PdSe2 monolayer possesses a moderate band gap of about 1.10 eV and high electron motilities of about 9800–42000 cm2v−1s−1, suitable for the electronic and optoelectronic devices working at infrared light region. The band gap of PdSe2 monolayer can be modulated by applying tensile strains. With the increase of tensile strain, the band gap decreases and comes to close as the tensile strain is larger than 14%. Consequently, the light adsorption ability of the PdSe2 monolayer in infrared light region is greatly enhanced. These findings are quite promising for application in electronic and optoelectronic devices.

Methods

Our first-principles calculations were performed within density-functional theory (DFT) using the Vienna ab initio simulation package known as the VASP code27,28,29. The projector augmented wave method (PAW)30,31 was used to describe the electronic-ion interaction. The energy cutoff of the plane waves was set to 450 eV with an energy precision of 10−5 eV. The electron exchange–correlation function was treated using a generalized gradient approximation (GGA) in the form proposed by Perdew, Burke, and Ernzerhof (PBE)32. The Monkhorst-Pack k-point meshes33 for the Brillouin zone (BZ) sampling used in structural optimization and electronic structure calculations are 8 × 8 × 1 and 15 × 15 × 1, respectively. The primitive cell contains one Pd atom and two Se atoms which is periodically repeated along the x- and y-directions. A vacuum region up to 15 Å was applied along the z-direction to exclude the interaction between adjacent images. Both atomic positions and lattice vectors were fully optimized using the conjugate gradient (CG) algorithm until the maximum atomic forces were less than 0.0005 eV/Å. The lattice constants of the orthorhombic PdSe2 crystal (a = 5.752 Å, b = 5.926 Å) obtained from our calculations agree well with the experimental data (a = 5.746 Å, b = 5.868 Å)12, confirming the validity of this strategy.

Additional Information

How to cite this article: Liu, X. et al. Strain-Modulated Electronic Structure and Infrared Light Adsorption in Palladium Diselenide Monolayer. Sci. Rep. 7, 39995; doi: 10.1038/srep39995 (2017).

Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.