Helium incorporation induced direct-gap silicides

The search of direct-gap Si-based semiconductors is of great interest due to the potential application in many technologically relevant fields. This work examines the incorporation of He as a possible route to form a direct band gap in Si. Structure predictions and first-principles calculations show that He and Si, at high pressure, form four dynamically stable phases of Si2He (oP36-Si2He, tP9-Si2He, mC18-Si2He, and mC12-Si2He). All phases adopt host–guest structures consisting of a channel-like Si host framework filled with He guest atoms. The Si frameworks in oP36-Si2He, tP9-Si2He, and mC12-Si2He could be retained to ambient pressure after removal of He, forming three pure Si allotropes. Among them, oP36-Si2He and mC12-Si2He exhibit direct band gaps of 1.24 and 1.34 eV, respectively, close to the optimal value (~1.3 eV) for solar cell applications. Analysis shows that mC12-Si2He with an electric dipole transition allowed band gap possesses higher absorption capacity than cubic diamond Si, which makes it to be a promising candidate material for thin-film solar cell.


INTRODUCTION
With the growth of population and the development of science and economy, human beings need more energy to create a better living environment. However, burning traditional fossil fuels is causing climate change, global warming, air pollution, acid rain, and a serious of other environmental problems [1][2][3][4] . Thus, energy becomes one of the most important issues on the international environment and development agenda. Photovoltaic modules provide a clean, reliable, and abundant way to convert solar energy into electricity to meet the growing demand for energy [5][6][7][8] . A good photovoltaic material should possess an electric dipole transition allowed direct band gap 9 and the Shockley-Queisser limit predicts that a band gap of 1.34 eV achieves the highest solar conversion efficiency (33.7%) for a single p-n junction 10 . Due to the relative abundance and environmental friendliness of silicon, silicon solar cells have attracted much attention in the field of photovoltaic market in the past several decades. However, the indirect electric band gap and the large optical gap (larger than 3 eV) make the thin-film silicon not a competitive candidate 11 . Thicker silicon can increase the efficiency of solar conversion but with a higher commercial cost 11,12 . Therefore, to search for potential Si allotropes or Si-based compounds with an electric dipole transition allowed direct band gap is of great interest.
Much effort has been devoted to the search for new Si allotropes with direct or quasi-direct band gaps  . A series of new Si structures formed by phase transformations under high pressure have been observed experimentally [13][14][15][16][17][18][19][20] . Direct-gap BC8-Si was formed after releasing the pressure from the high-pressure β-Sn phase to 2 GPa 13 . However, the relatively narrow direct band gap of 30 meV precludes BC8-Si as a photovoltaic material 18 . Irradiation of amorphous Si film with a coherent electron beam stabilized a new Si 9 phase with a direct band gap of~1.59 eV, indicating a potentially useful photovoltaic material 20 . In particular, the hexagonal 2H-allotrope phase was well studied both theoretically 35 and experimentally [36][37][38][39] and can be viewed as a better potential photovoltaic material than cubic silicon.
Si , and He-NH 3 [50][51][52] . Although most of these materials are predicted under extreme condition, the results provide a clear indication that He can break through the chemical inert barrier and react with other substances. The incorporation of inert He tends to form open framework structures with weak interactions between He and the host sublattice. For example, our previous calculations predicted a HeN 4 compound formed at high pressure 42 , which consists of open channels of N atoms holding He. Their weak interactions allow the removal of the He from the structure, leading to a pure t-N structure. Therefore, He may be regarded as a good intermediate for preparing new materials. A recent molecular dynamics (MD) simulation has demonstrated that Si and He react to form hP6-Si 2 He at 7 GPa and 1500 K 53 , which is a host-guest structure compared by a hexagonal diamond Si sublattice encapsulating He atoms. In addition, the scientists screened a series of stable potential photovoltaic Si phase by substituting other atoms, including He atom 54 . These results, especially for the t-N phase and Si 24 obtained from high-pressure phases of HeN 4 42 and Na 4 Si 24 34 , respectively, give us a clear indication of the reaction between He and other substances and motivate us to study whether new Si allotropes could be formed from high pressure Si-He compounds.
This work reports extensive structure searches on Si 2 He which uncover four energetically favorable channel-like phases (oP36-Si 2 He, tP9-Si 2 He, mC18-Si 2 He, and mC12-Si 2 He) in addition to hP6-Si 2 He 53 . The He atoms trapped inside the channels are easily removed from oP36-Si 2 He, tP9-Si 2 He, and mC12-Si 2 He to form oC24-Si, tP6-Si, and mC8-Si, respectively. Interestingly, oP36-Si 2 He and mC12-Si 2 He are direct-gap semiconductors with band gaps of 1.24 and 1.34 eV, respectively, proximately to the Shockley-Queisser limit (1.34 eV). In particular, mC12-Si 2 He has an electric dipole transition allowed direct band gap, making it a good candidate photovoltaic material.

RESULTS
Crystal structure searches Structure predictions are first performed for Si 2 He at 10 GPa with a maximum of eight formula units (f.u.) in a simulation cell. The previously proposed hP6-Si 2 He 53 is successfully predicted, but with much higher enthalpy, as shown in Fig. 1. Instead, the four structures we predicted are energetically favorable than hP6-Si 2 He 53 . Crystal structures of four phases are shown in Fig. 2 and the lattice parameters of these structures are listed in the Supplementary Table 1. The four structures with increasing energy are oP36-Si 2 He, tP9-Si 2 He, mC18-Si 2 He, and mC12-Si 2 He, namelỹ 0.13,~0.08,~0.05, and~0.04 eV/f.u. energetically lower than hP6-Si 2 He 53 at 10 GPa, respectively. We also calculate the related enthalpies of Si-He compounds as a functions of pressure by including different van der Vaals (vdW) functionals (optPBE-vdW, optB88-vdW, and DFT-D3) 55,56 , as shown in Supplementary Fig. 1. The results reveals that the vdW interaction almost has no influence in the phase transition sequence of Si 2 He. Static-lattice enthalpy calculations reveal that oP36-Si 2 He remains energetically most stable up to 18 GPa, above which hP6-Si 2 He 53 takes over, see Fig. 1. A previous MD simulation suggests that hP6-Si 2 He 53 could be formed at 7 GPa and 1500 K. Therefore, we examine the effect of temperature on the relative stability using the quasi-harmonic approximation and find that temperature does not change the phase diagram of Si 2 He, but rather postpones the transition pressure to 26 GPa at 1500 K. This result indicates that the predicted four phases are more favorable than hP6-Si 2 He in experimental synthesis at low pressures. The MD calculations also include vdW interactions.

Structural configurations of predicted phases
All structures are channel frameworks composed of four coordination Si atoms and filled with He atoms in the voids, as shown in Fig. 2. The energetically most stable structure oP36-Si 2 He is orthorhombic with space group Pnnm (12 f.u. in a unit cell), as shown in Fig. 2a. The Si sublattice of oP36-Si 2 He along the a-axis shows a one-dimensional channel structure composed of ten-, six-, and five-membered rings. The Si-Si bond lengths are ranging from 2.28 to 2.33 Å, slightly shorter than that of hP6-Si 2 He (2.35 Å) 53 . Helium atoms are stacked in triangles in quasi-circular channels of ten membered rings (see Supplementary Fig. 2). The triclinic tP9-Si 2 He has a symmetry of P3 2 12 (3 f.u. in a unit cell), as shown in Fig. 2b. The silicon atoms form a spiral staircase configuration with a six-membered circular channel, and the helium atoms are distributed in three vertical columns in the channel with the He-He distance of 2.34 Å. The mC18-Si 2 He phase is monoclinic with the symmetry of C2/m (6 f.u. in a unit cell). The Si atoms form six-and five-membered rings, and two sixmembered rings are connected by two layers of five-membered rings dislocated and stacked along the c-axis, as shown in Fig. 2c. The Si-Si bond lengths are ranging from 2.30 to 2.37 Å. The He atoms form a tilted triangle arranged along the channel. The mC12-Si 2 He is monoclinic with space group C2/m (4 f.u. in a unit cell), as shown in Fig. 2d. Two kinds of channels sharing edges are found along the b-axis formed by fiveor seven-membered rings of Si atoms. A zigzag arrangement of He atoms is located inside the larger channels formed by the seven-membered rings. The shortest distances between He and the Si channel in structures of oP36-Si 2 He, tP9-Si 2 He, mC18-Si 2 He, and mC12-Si 2 He are 2.73, 2.56, 2.64, and 2.49 Å, respectively, which are shorter than the Na-Si distance (3.01 Å) in Na 4 Si 24 34 . Similar host-guest structures have been reported in several other compounds, such as Na 4 Si 24 34 and HeN 4 42 . The previously proposed hP6-Si 2 He 53 can also be regarded as a host-guest structure with a distorted diamond hexagonal host Si sublattice encapsulating guest He atoms inside the hexagonal channels. The lowest enthalpy of oP36-Si 2 He compared with hP6-Si 2 He suggests that Si can form larger channels for the incorporation of He. The dynamic stability of oP36-Si 2 He, tP9-Si 2 He, mC18-Si 2 He, and mC12-Si 2   The MD simulation (with the vdW interaction) reveals that all structures exhibit thermodynamic stability at ambient pressure and temperature (300 K), suggesting that all of them could be quenched and recovered at ambient conditions once formed (see Supplementary Fig. 6).
Charge transfer and CI-NEB energy barrier of silicides Electron localization function calculations exclude the existence of Si-He covalent bonds in both compounds given the absence of electron localization between them (see Supplementary Fig. 3). Bader charge analysis 57 suggests slight charge transfer from the Si framework to each He atom of (0.03 electrons in oP36-Si 2 He, 0.05 electrons in tP9-Si 2 He, 0.09 electrons in mC18-Si 2 He, and 0.05 electrons in mC12-Si 2 He), similar to those predicted in Na 2 He 40 and FeO 2 He 45 . The weak interaction between the Si frameworks and He atoms provides a good priori condition for removal of the He from the structures, but the process can also be influenced by different Si frameworks. Therefore, we examine the energy barriers of He diffusing along the channels, see Fig. 3a. CI-NEB calculates energy barriers of 0.08, 0.01, 1.51, and 0.37 eV for oP36-Si 2 He, tP9-Si 2 He, mC18-Si 2 He, and mC12-Si 2 He, respectively. We also checked the calculations with including vdW interaction, as shown in Supplementary Table 3. The vdW interaction has no effect on the energy barrier of all structures.The energy barriers of all structures except mC18-Si 2 He are much lower than that (0.74 eV) of Na 4 Si 24 for removing Na 34 , see Fig. 3b and Supplementary Fig. 7 (with the vdW interaction), indicating comparatively easy removal of He atoms from oP36-Si 2 He, tP9-Si 2 He, and mC12-Si 2 He. For the mC18-Si 2 He, there exhibits a hexagonal channel structure both along a-and b-axis with a diameter of only about 3.9 Å and is much shorter than that of oP36-Si 2 He (6.4 Å), which induces a high energy barrier of 1.51 eV and indicates that He is difficult to be removed. This suggests that the structural configuration also plays a very important role in removing helium atoms. Figure 4a-c shows three pure Si structures obtained by removing He from oP36-Si 2 He, tP9-Si 2 He, and mC12-Si 2 He,    denoted as oC24-Si, tP6-Si, and mC8-Si, respectively. Both Si allotropes retain Si frameworks nearly identical to those of the corresponding compounds. Phonon dispersion calculations confirm the stability of three allotropes (see Supplementary Fig. 4). A literature survey surprisingly found that these three Si structures have been previously predicted with much higher energies (~80 meV) than CD-Si 21,58,59 . Metastable structures with higher energies are generally difficult to synthesize directly. Here, we provide a potential chemical pathway for the synthesis these metastable Si allotropes, namely removing He atoms from pressure-stabilized Si-He compounds by thermal degassing.

Electronic and optical properties
Photovoltaic materials require a suitable direct band gap to ensure a large overlap with the solar spectrum in the visible range, and thus strong solar absorption. Electronic band gaps of the compounds are calculated by using the HSE06 functional and the band structures are shown in Fig. 5 Supplementary Fig. 3, we can see that when we include the vdW interaction, the electronic band gaps change a little. Take mC12-Si 2 He as an example, the band gap is about 1.35 eV (with the vdW interaction), while is 1.34 eV without considering vdW interaction. From our calculations (see Fig. 5), we can clearly find that tP9-Si 2 He and mC18-Si 2 He are indirect-gap semiconductors with indirect band gaps of 2.18 and 0.91 eV, respectively, which excludes the possibility of being good photovoltaic materials. Interestingly, oP36-Si 2 He and mC12-Si 2 He have direct band gaps of 1.24 and 1.34 eV, respectively, close to the Shockley-Queisser limit (1.34 eV), which indicate that they can be viewed as good potential photovoltaic materials. We also calculated the Si allotropes electronic band structure after the removal of He atoms in oP36-Si 2 He, tP9-Si 2 He, and mC12-Si 2 He (see Fig. 6). After removing the He atoms, the electronic band gaps of these Si allotropes decrease and degenerate from the direct band gaps to the indirect band gaps. As shown in Fig. 6, the band gap of oC24-Si can be viewed as a quasi-direct gap with a value of 0.95 eV, while for tP6-Si and mC8-Si are indirect with values of 2.12 and 0.84 eV, respectively. These results reveal that the incorporation of He benefits to forming the direct-gap semiconductor compounds for the Si-He system. To evaluate the sunlight absorption abilities of a direct band gap material, the imaginary parts of the dielectric constant of oP36-Si 2 He, mC12-Si 2 He and three silicon allotropes (oC24-Si, tP6-Si, and mC8-Si) were calculated by HSE06 functional, compared with that of CD-Si, as shown in Fig. 7. We also checked the results with the independent-quasiparticle approximation and solving the Bethe-Salpeter equation (BSE) to include excitonic and local-field effects 61 . The HSE06 results are in good agreement with that was obtained by GW + BSE method. The GW + BSE results are shown in Supplementary Fig. 8. The calculation results show that the absorption spectra of oP36-Si 2 He is slightly higher than that of mC12-Si 2 He and both have much better solar absorption capacities than the other three silicon allotropes and the CD-Si, as indicated by their broader overlap with the AM1.5 solar spectrum 62 . The optical absorption in oP36-Si 2 He and mC12-Si 2 He have an increasing trend at 1.2 and 1.4 eV, respectively. Another critical factor for a good Fig. 7 Optical properties of the predicted Si 2 He and Si allotropes. Imaginary part of the dielectric functions of oP36-Si 2 He, mC12-Si 2 He, and the three silicon alltropes (oC24-Si, tP6-Si, and mC8-Si) calculated with the HSE06 functional, as well as the reference air mass 1.5 (AM1.5) solar spectral irradiance 62 and CD-Si. photovoltaic material is a dipole-allowed direct transition. Therefore, further calculation of the square of the transition dipole moment (P 2 ) explores the transition permissibility between the direct band gaps (see the lower panels in Figs. 5 and 6). The direct band gap of oP36-Si 2 He is located at Γ point in the first Brillouin zone, and the P 2 at Γ point is close to 0, which indicates that oP36-Si 2 He is dipole-forbidden and same to the other three silicon allotropes (oC24-Si, tP6-Si, and mC8-Si). Instead, mC12-Si 2 He shows a dipole-allowed direct transition with large P 2 value at the Γ point, suggesting good potential as a photovoltaic material.
Other predicted Si-He compounds To search for other possible Si-He compounds, structural predictions are also performed for Si 3 He and Si 4 He at 10 GPa using a maximum of 20 atoms in a simulation cell. Supplementary  Fig. 9 summarizes the formation enthalpies of the stoichiometries with respect to decomposition into β-Sn Si and hcp He. Unfortunately, the formation enthalpy of all the Si-He compounds are positive. In fact, this does not completely rule out the possibility of experimental synthesis. A recent data mining study found that more than 60th percentile of the 0 K DFT-calculated metastability of all of the compounds within the Inorganic Crystal Structure Database was 150 meV/atom above the convex hull 63 . Actually, some silicon-contained compounds with high formation enthalpy have been successfully experimentally synthesized. For example, the theoretical calculated formation enthalpy of clathrate (type-I) I 9.5 Si 46 is above convex hull 130 meV/atom, and SiB 6 has the formation enthalpy of 289 meV/atom, both of which have been synthesized [64][65][66][67] . The crystal structures and electronic structures of Si 3 He and Si 4 He are shown in Supplementary Figs. 10-13. The formation enthalpies of Si 3 He and Si 4 He phases are both <130 meV/atom and they have direct band gap, which could be potential photovoltaic materials.

DISCUSSION
He, which has two electrons, is the most chemically inert natural element, although several recent works have predicted or synthesized He-containing compounds 42,53 . Despite this, He can be regarded as chemically inert in Si-He, as the atoms are almost completely independent of the surrounding structure with negligible charge gained from Si. He appears to be chemically inert in all its known compounds (e.g., Na 2 He 40 and HeN 4 42 ), allowing it to be removed easily from the surrounding structure without changing the structure substantially. Interestingly, the incorporation of He in Si allotrope can form direct band gap semiconductors with the suitable band gaps, with the dipoleallowed direct band gap confirmed by mC12-Si 2 He. Therefore, He appears to be a good intermediate for designing potential functional materials.
In conclusion, through extensive structure searches of Si 2 He systems, we predict four dynamically stable phases (oP36-Si 2 He, tP9-Si 2 He, mC18-Si 2 He, and mC12-Si 2 He) with open framework structures comprising Si channels containing triangle or zigzag arrangements of He atoms. CI-NEB calculations reveal that the He atoms could be easily removed along the channels in them to leave the pure Si allotropes, oC24-Si, tP6-Si, and mC8-Si, respectively. oP36-Si 2 He and mC12-Si 2 He exhibit direct-gap semiconductive property, while others possess indirect band gaps. The dipole-allowed direct band gap of 1.34 eV in mC12-Si 2 He makes it a potential thin-film photovoltaic material. The current results demonstrate that He is an excellent element for regulating the properties of materials, as well as a good medium to synthesize functional materials.

Electronic and optical properties calculations
The Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional was employed to correct the electronic band structures 83 and calculate the optical properties. We also make a test of the Fock exchange percentage to check its accuracy with GW method 60 and the Fock exchange percentage is adopted the defaut value of 0.25. All electron projector augmented wave pseudopotentials with 1s 2 and 3s 2 3p 2 valence configurations were chosen for He and Si atoms, respectively 84 . A plane wave cutoff energy of 800 eV and k-point mesh of 2π × 0.03 Å −1 were set to ensure total energy and forces convergence better than 1 meV/atom and 1 meV/Å, respectively. VASPKIT 85 was used to resolve the results of the transition dipole moment and the optical absorption spectra (the imaginary part of the dielectric function, ε 2 ). Specially, we have checked our calculations (structural relaxation, band gap calculation, MD, and CI-NEB) with including the vdW interactions 56 .