Plasmon excitation in hydrogenated silicene nanostructures Open Access

Silicene, which is a kind of monolayer silicon film in a buckled honeycomb lattice, represents a monoelemental class of two-dimensional materials similar to graphene.^1–12 Because of its exotic electronic properties and compatibility with current silicon-based electronics, it has been attracting people’s attention in recent years. Before graphene became a research hotspot, the planarity of the two-dimensional silicon layer had been theoretically investigated.³ First-principles calculations of structure optimization, phonon modes, and finite temperature molecular dynamics predict that silicon can have stable, two-dimensional, low-buckled, honeycomb structures.¹³ Experimentally, through different methods, silicene has been synthesized. Due to the absence of a graphite-like form of silicon in nature, silicene is synthesized by epitaxial growth on a substrate. At present, thermal evaporation on a substrate, surface segregation from a substrate, and intercalation through a silicide network have been implemented for the production of silicene.^14–16 Chemical functionalizations, especially hydrogenation, are used to tailor the electronic properties of silicene effectively.^17–19 It has been reported that, in the hydrogenated silicene sheets, the silicon atoms form different conformations, such as the chair and Z-line conformations.¹⁸ The bandgap of silicene can be tuned by varying hydrogen coverage, which is of the utmost importance for electronic applications.

At present, more and more attention has been paid to the research of plasmons in micro- and nanomaterials.^20–22 This is mainly because the plasmons in micro- and nanomaterials have a series of novel optical properties, such as local electric field enhancement, which have important application prospects in energy, sensor detection, information, and other fields. Silicene, as with graphene, is a promising plasmonic material.^23–28 By using the time-dependent density functional theory within the random phase approximation, this study shows that intrinsic silicene also has two plasmon resonance bands, which are, respectively, π and π–σ plasmon resonance bands.²³ Compared to monolayer silicene, stacked bilayer silicene has lower plasmon resonance excitation.²⁵ Theoretically, Zhang et al. studied the effects of defect, doping, geometrical configuration, and size on plasmon excitations for three silicon nanostructures.²⁴ These nanostructures are, respectively, silicene, siliconeet, and dumbbell silicene. They found that plasmon excitations of these nanostructures are rather sensitive to the polarization direction. Compared with triangular and hexagonal nanostructures, the rectangular silicene nanostructure is the best choice for plasmonic materials. Our previous study found that, for the silicene nanostructure, because delocalized π electrons participate in two plasmon bands excitation, with an increase in the side length of the rectangular silicene nanostructure along the excitation direction, two main plasmon bands are red-shifted.²⁹ For silicene nanostructure dimers, within a certain gap distance, a long-range charge transfer plasmon mode appears.³⁰ 

In this paper, we systematically studied the plasmon excitation in hydrogenated silicene nanostructures. Chair and Z-line conformations of the hydrogenated silicene nanostructure are mainly considered. The evolution of the plasmon excitation mode of the system is studied with an increase in the hydrogenation degree. The studies provide theoretical support for the practical application of silicene nano-optoelectronic devices.

All of our calculations were performed with time-dependent density functional theory code OCTOPUS.³¹ The plasmon excitation of different nanomaterials has been successfully predicted by the time-dependent density functional theory.²³ In our calculations, silicon atom and hydrogen atom were described by the Troullier–Martins pseudopotentials.³² Local density approximation (LDA)³³ for the exchange-correlation was used in both the ground state and the excited state calculations. The simulation zone was defined by assigning a sphere around each atom with a radius of 0.9 nm and a uniform mesh grid of 0.03 nm. In the real time propagation, the excitation spectrum was extracted by the Fourier transform of the dipole strength induced by an impulse excitation.³¹ In the real-time propagation, the electronic wave packets were evolved for typically 8000 steps with a time step of Δt = 0.005ℏ/eV. We mainly investigate the plasmon excitation in the direction that is parallel to the plane of the silicene nanostructure.

Two different kinds of stable hydrogenated silicene nanostructures are studied. Schematic diagrams of the first kind of the hydrogenated silicene nanostructures are shown in Fig. 1, which are of the chair conformation. Compared with the same size pure nanostructures,²⁹ hydrogenated silicene nanostructures have the following characteristics. When the whole nanostructures are hydrogenated, the morphology remains unchanged, and are still planar as a whole, as shown by the A quantum dot in Fig. 1. The H–Si bond length and Si–Si bond length are, respectively, 0.15 nm and 0.2326 nm. Compared with the pure nanostructures, the Si–Si bond length increased by 0.0073 nm. In the side view of hydrogenated silicene nanostructures, the average distance between the upper and lower layers of silicon atoms is equal to 0.073 nm, which increases by about 0.028 nm compared with the pure Si nanostructures. When hydrogenation occurs in the boundary, the morphology of the system is almost unchanged, and are also still planar. However, when hydrogenation occurs in other parts, the nanostructure has different degrees of bending, as shown in Fig. 1. Among them, D, E, and F are the schematic diagrams of the nanostructures that hydrogenated gradually along one end. The result shows that there is a certain angle between the hydrogenated part plane and the non-hydrogenated part plane. For D and F nanostructures, the angle is about 148.5°, while for the E nanostructure, the angle is about 144°. With an increase in the hydrogenation degree, the angle between the two planes first decreases, and then, increases. In other words, when half of the nanostructure is hydrogenated along one end, the first kind hydrogenated silicene nanostructures are bent to the maximum extent.

Figure 2 shows the optical absorption of different hydrogenated silicene nanostructures to an impulse excitation polarized in the armchair-edge (a) and zigzag-edge (b) directions. First, we analyze the characteristics of the low energy plasmon. Compared with the pure silicene nanostructures, when the whole nanostructures are hydrogenated, the delocalized π electrons disappear and correspondingly form sp³ hybrid orbitals. Therefore, the low energy plasmon resonance mode near 2.0 eV disappears. In Figure 2(a), D, E, and F show that, when an impulse excitation is polarized in the armchair-edge direction, with an increase in the hydrogenation degree, the motion length of the delocalized π electrons decreases gradually, and the resonance intensity of low-energy plasmon decreases gradually. The plasmon excitons gradually disappear along the low energy end. In Figure 2(b), D, E, and F show that, when an impulse excitation is polarized in the zigzag-edge direction, with an increase in hydrogenation degree, although the resonance intensity of the whole low-energy plasmon resonance band decreases and disappears gradually, the whole low-energy plasmon resonance band does not disappear along the low-energy end. The reason is that, the motion length of the delocalized π electrons is basically unchanged in such a situation. Compared with the pure nanostructures, when the silicene nanostructures are hydrogenated in the middle area, the resonance intensity of low-energy plasmon is only slightly reduced. However, when the silicene nanostructures are hydrogenated in the boundary area, the resonance intensity of low-energy plasmon decreases greatly, and disappears along the low-energy end, as shown in Fig. 2 B and C. In the case of boundary hydrogenation, compared with the pure nanostructure,²⁹ when the impulse excitation is polarized in the armchair-edge direction, the low energy plasmon resonance mode at 0.43 eV disappears, and the other two resonance peaks at 1.58 eV and 2.37 eV have a blue shift. When the impulse excitation is polarized in the zigzag-edge direction, the low energy plasmon resonance is almost suppressed. There is only a small absorption peak at 2.25 eV. In the case of middle hydrogenation, when the impulse excitation is polarized in the armchair-edge direction, compared with the pure nanostructure, although the resonance near 0.43 eV disappeared, and the resonance intensity of other low-energy resonance bands also decreased, a strong resonance absorption peak appeared near 1.02 eV. When the impulse excitation is polarized in the zigzag-edge direction, a resonance appears near the lower 0.85 eV.

Then, for the first kind hydrogenated silicene nanostructures, we analyze the characteristics of the high energy plasmon. When the impulse excitation is polarized in the armchair-edge direction, compared with pure nanostructures,²⁹ the band of high energy plasmon resonance spreads toward the low energy end. However, the main high plasmon resonance peak has a blue shift. The main high plasmon resonance peak of completely hydrogenated silicene nanostructure is at 7.76 eV, while the main high plasmon resonance peak of the pure silicene nanostructure of the same size is at 5.86 eV. Compared with hydrogenation in the central area, when hydrogenation occurs in the boundary, the high-energy plasmon extends to the low-energy end more. When hydrogenation occurs gradually along one end, the main high plasmon resonance peak moves toward blue gradually, as shown in Fig. 2(a) D, E, and F. When the impulse excitation is polarized in the zigzag-edge direction, compared with pure nanostructures, the band of high energy plasmon resonance also spreads toward the low energy end. The two main high plasmon resonance peaks of the completely hydrogenated silicene nanostructure are at 5.65 eV and 7.94 eV, while two main high plasmon resonance peaks of the pure silicene nanostructure of the same size are at 6.5 eV and 8.0 eV. In addition, compared with pure silicene nanostructures, the intensities of the two main high plasmon resonance peaks of the completely hydrogenated silicene nanostructure have changed. For the pure silicene nanostructure, the intensities of the two high plasmon resonance peaks are almost the same. However, for a completely hydrogenated silicene nanostructure, the intensity of the plasmon resonance peak of 5.65 eV is only 50% of the intensity of the plasmon resonance peak of 7.94 eV.

In order to further explain the plasmon resonance mechanism of different hydrogenated silicene nanostructures, we calculated the induced charge density distribution. The frequency dependent induced charge density response is obtained by taking the Fourier transform $Δρ(r,ω)=1T∫0T[ρ(r,t)−ρ(r,0)]eiωtdt$⁠, where T is the total computation time. Figure 3 shows the Fourier transform of the induced charge density for the B hydrogenated silicene nanostructure, as shown in Fig. 1, when the excitation is polarized in the armchair-edge direction, at the energy resonance points 1.58 eV (a) and 7.91 eV (b), respectively. Figure 4 shows the Fourier transform of the induced charge density for the C hydrogenated silicene nanostructure, when the excitation is polarized in the armchair-edge direction, at the energy resonance points 1.03 eV (a) and 7.39 eV(b), respectively. In Figs. 3 and 4, the induced density plane is parallel to the hydrogenated silicene nanostructures, and the vertical distance between the central plane of hydrogenated silicene nanostructures and this induced density plane is 0.24 nm. For B and C hydrogenated silicene nanostructures, the induced charge distribution has some common characteristics. First, the induced charge density distribution corresponding to each plasmon resonance mode has the characteristic of dipole-like resonance. This is mainly due to the fact that, along the excitation direction, the delocalized π electrons participate in the resonance excitation of high energy and low energy plasmons. The π electrons can vibrate back and forth in a long distance along the excitation direction. Second, in some regions, the induced charge density distribution shows an oscillatory behavior. On the one hand, it is due to the local binding of silicon atom potential, on the other hand, it is due to the valence electrons forming sp² and sp³ hybrid orbits. For the B nanostructure that is hydrogenated in the boundary region and the C nanostructure that is hydrogenated in the middle area, the induced charge distribution also has some different characteristics. The main different characteristic is that, for the B nanostructure, the induced charge density is mainly distributed in the middle region of the nanostructure. This is mainly because the valence electron forms a sp³ hybrid orbit in the boundary region. The delocalized π electrons vibrate back and forth in the middle region of the nanostructure.

Schematic diagrams of the second kind hydrogenated silicene nanostructures, which are of the Z-line conformation, are shown in Fig. 5. The left picture of each quantum dot is the side view of the quantum dot along the zigzag-edge direction, the middle picture is the top view of the quantum dot, and the right picture is the side view along the lower left corner, as shown in the middle picture. When the whole nanostructures are hydrogenated, the morphology remains unchanged, and is still planar as a whole. Compared with the first kind hydrogenated silicene nanostructures, there are little changes in the H–Si bond length and Si–Si bond length. In the side view of the second kind A hydrogenated silicene nanostructures, the average longitudinal distance between the upper and lower layers of silicon atoms is equal to 0.194 nm, which increases by about 0.121 nm compared with the first kind hydrogenated A silicene nanostructures. When hydrogenation occurs in the boundary, the morphology of the system is still planar as a whole. However, when the hydrogenation occurs in other ways, the nanostructures have different degrees of bending, as shown in Fig. 5.

Figure 6 shows the optical absorption of different second kind hydrogenated silicene nanostructures to an impulse excitation polarized in the armchair-edge (a) and zigzag-edge (b) directions. The results show that, for the low energy plasmon excitons, the evolution laws of the two kinds of hydrogenated silicene nanostructures are basically the same along with the hydrogenation change. For the high energy plasmon excitons, when the whole nanostructures are hydrogenated, unlike the first kind of the hydrogenated silicene nanostructures, both the resonance band and the main absorption peak of the high energy plasmon of the second kind hydrogenated silicene nanostructures have a blue shift. The blue shift shows that the number of free π electrons involved in high energy resonance has been reduced. When impulse excitation is polarized in the armchair-edge direction, the degree of the blue shift of the main absorption peak of the high energy plasmon is small. Along the zigzag-edge direction, when the whole nanostructures are hydrogenated, there is only one large plasmon resonance band, and the absorption peak at the low energy end of the resonance band is at 7.6 eV, which is significantly divergent from the pure silicene nanostructure and the first kind hydrogenated silicene nanostructures.

Using the time-dependent density functional theory, we have carried out a systematic study of plasmon excitations of the two kinds of hydrogenated silicene nanostructures and mainly investigated the impacts of the hydrogenation method and hydrogenation concentration on the plasmon excitations. Based on these calculations and results, the following conclusions can be drawn. In the low energy region, the plasmon excitation evolution laws of the two kinds of hydrogenated silicene nanostructures are basically the same. When the whole nanostructure is hydrogenated, because the delocalized π electrons disappear and correspondingly form sp³ hybrid orbitals, the low energy plasmon resonance mode near 2.0 eV disappears. When the hydrogenation occurs in the middle area of the silicene nanostructure, the resonance intensity of low-energy plasmon is only slightly reduced. However, when the hydrogenation occurs in the boundary area, the resonance intensity of low-energy plasmon decreases greatly. In the high energy region, different hydrogenation methods have different effects on plasmon excitation. For the first kind of hydrogenated silicene nanostructure, compared with pure silicene nanostructures, no matter in which direction the impulse excitation is polarized, the band of high energy plasmon resonance spreads toward the low energy end, and the main high plasmon resonance peak locates in much higher energy area. For the second kind hydrogenated silicene nanostructures, when the whole nanostructures are hydrogenated, both the resonance band and the main absorption peak of the high energy plasmon have a blue shift. In addition, when the impulse excitation is polarized in the zigzag-edge direction, there is only one large plasmon resonance band that is significantly different from the pure silicene nanostructure and the first kind hydrogenated silicene nanostructures. Moreover, for the two kinds of hydrogenated silicene nanostructures, when the whole nanostructures are hydrogenated, the morphology is still planar as a whole. However, when hydrogenation occurs in other ways, the curling deformation of the second kind hydrogenated silicene nanostructures is more serious.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

We acknowledge financial support from major research projects of innovative groups in the Education Department of the Guizhou Province of China [Qian Jiao He K. Y. Zi (2018) Grant No. 035], and the National Natural Science Foundation of China (Grant No. 11464023).