Helium Incorporation Stabilized Direct-gap Silicides
Shicong Ding, Jingming Shi, Jiahao Xie, Wenwen Cui, Pan Zhang, Kang Yang, Jian Hao, Meiling Xu, Qingxin Zeng, Lijun Zhang, Yinwei Li
HHelium Incorporation Stabilized Direct-gap Silicides
Shicong Ding, Jingming Shi, ∗ Jiahao Xie, Wenwen Cui, Pan Zhang, KangYang, Jian Hao, Meiling Xu, Qingxin Zeng, Lijun Zhang, and Yinwei Li † Laboratory of Quantum Materials Design and Application, School of Physicsand Electronic Engineering, Jiangsu Normal University, Xuzhou 221116, China State Key Laboratory of Superhard Materials, Key Laboratory of Automobile Materials of MOE,and College of Materials Science and Engineering, Jilin University, Changchun 130012, China (Dated: June 12, 2020)The search of direct-gap Si-based semiconductors is of great interest due to the potential appli-cation in many technologically relevant fields. This work examines the incorporation of He as apossible route to form a direct band gap in Si. Structure predictions and first-principles calculationshave shown that He reacts with Si at high pressure, to form the stable compounds Si He and Si He.Both compounds have host-guest structures consisting of a channel-like Si host framework filledwith He guest atoms. The Si frameworks in two compounds could be persisted to ambient pressureafter removal of He, forming two pure Si allotropes. Both Si–He compounds and both Si allotropesexhibit direct or quasi-direct band gaps of 0.84–1.34 eV, close to the optimal value ( ∼ He with an electric-dipole-transition allowed bandgap possesses higher absorption capacity than diamond cubic Si, which makes it to be a promisingcandidate material for thin-film solar cell.
Pollution-free renewable energy is urgently needed asa substitute for fossil fuels. Inexhaustible solar energy iswidely used, and its conversion to electricity for daily userequires photovoltaic materials.
Cubic diamond silicon(CD-Si) is a good candidate photovoltaic material due toits suitable band gap and stability. A good photovoltaicmaterial should possess an electric-dipole-transition al-lowed direct band gap. The Shockley-Queisser limit predicts that a band gap of 1.34 eV achieves the high-est solar conversion efficiency (33.7%). However, CD-Siis an indirect-gap (1.17 eV) semiconductor, and thus notideal for thin-film photovoltaic devices. Therefore, thesearch for new Si allotropes or Si-based compounds withan electric-dipole-transition allowed direct band gap is ofgreat interest.Much effort has been devoted to the search for newSi allotropes with direct or quasi-direct band gaps.
A series of new Si structures formed by phase transfor-mations under high pressure have been observed experi-mentally.
In particular, direct-gap BC8-Si was formedafter releasing the pressure from the high-pressure β -Snphase to 2 GPa. However, the relatively narrow directband gap of 30 meV precludes BC8-Si as a photovoltaicmaterial. Irradiation of amorphous Si film with a co-herent electron beam stabilized a new Si phase with adirect band gap of approximately 1.59 eV, indicating apotentially useful photovoltaic material. First-principle calculations are important in the searchfor new Si structures. Structure searches based on Crys-tal structure AnaLYSis by Particle Swarm Optimization(CALYPSO) have found four channel-like Si allotropes(oF16-Si, tP16-Si, mC12-Si, and tI16-Si) with directband gaps of 0.81–1.25 eV. A cubic Si -T phase with ∗ [email protected] † yinwei [email protected] a quasi-direct band gap of 1.55 eV was designed usinga new inverse-band-structure design approach based onCALYPSO. Conformational space annealing calcula-tions have uncovered two new Si allotropes, Q135 andD135, with direct band gaps of 0.98 and 1.33 eV, re-spectively, both of which were proposed to be good pho-tovoltaic materials with estimated photovoltaic efficiencyof ∼ Ab initio random structure searching has alsorevealed a new Si structure with space group
P bam anda direct band gap of 1.4 eV. By substituting C or Geatoms in their structures with Si atoms, at least 17 can-didate structures were predicted, of which nine (M585,
P bam -32, P /mmm , Im ¯3 m , C /c , I /mcm , I /mmm , P /m , and P /mbm ) have direct band gapsof 0.65–1.51 eV. Ab initio minima hopping structure pre-dictions have also predicted more than 44 Si structures, ofwhich eleven ( R ¯3 m -1, R ¯3 m -2, C /m , Immm -1,
Immm -2,
Immm -3,
P mma , I md , P nma , I ¯42 d and I )exhibit direct band gaps of 1.0–1.8 eV. All these di-rect or quasi-direct Si structures are metastable, possess-ing a high energy relative to CD-Si, and thus are difficultto synthesize directly.Si-rich compounds with open-framework structuresformed at high pressures are good precursors to obtainnew Si allotropes. A two-step synthesis method hasmade two metastable allotropes (a clathrate Si and achannel-like Si ) by removing Na from high-pressureNa–Si compounds. Channel-like Si was prepared byfirst synthesizing at high pressure a Na Si precursorthat contained a channel-like sp Si host structure filledwith linear Na chains. Na atoms were removed alongthe open channels via thermal degassing, leaving thepure Si allotrope. Electrical conductivity and opticalabsorption measurements confirmed a quasi-direct bandgap of 1.3 eV, making Si a potential photovoltaic ma-terial.The noble gas He becomes reactive at high pres- a r X i v : . [ c ond - m a t . m t r l - s c i ] J un FIG. 1. (a)
Enthalpy of mC24-Si He relative to previouslyproposed hP6-Si He as a function of pressure at 0 and 1500K. Arrows represent the phase transition pressures. (b) For-mation enthalpy of Si x He y ( x = 1–12 and y = 1–4) with re-spect to mC24-Si He and CD-Si at 10 GPa, defined as ∆ H =[ H (He x Si y ) – xH (Si He) – ( y – 2 x ) H (Si)] / ( x + y ). Crossesrepresent energetically unstable structures. Compounds withformation enthalpies higher than 0.02 eV/atom are not shown. sure, leading to several new compounds, includingNa He, HeN , He–alkali oxides (sulfides), He–Fe, FeO He, Mg(Ca)F , He–H O, and He–NH . The incorporation of inert He tends to form open-framework structures with weak interactions between Heand the host sublattice. For example, our previous cal-culations predicted a HeN compound formed at highpressure, which consists of open channels of N atomsholding He. Their weak interactions allow the removalof the He from the structure, leading to a pure t -N struc-ture. Therefore, He may be regarded as a good inter-mediate for preparing new materials. The t -N phase ob-tained from high-pressure HeN motivated us to studywhether new Si allotropes could be formed from highpressure Si–He compounds. A recent molecular dynam-ics (MD) simulation has demonstrated that Si and Hereact to form hP6-Si He at 7 GPa and 1500 K, whichis a host-guest structure comprising a hexagonal diamondSi sublattice encapsulating He atoms.This work reports extensive structure searches on Si–He systems that predict two stable channel-like com-pounds (mC24-Si He and mC16-Si He) in addition tohP6-Si He. The He atoms trapped inside the channels
FIG. 2. Crystal structures of (a) mC24-Si He, (b) mC16-Si He, (c) mC16-Si, and (d) mC12-Si. Black and greenspheres represent He and Si atoms, respectively. are easily removed from mC24-Si He and mC16-Si He toform mC16-Si and mC12-Si, respectively. Interestingly,mC24-Si He, mC16-Si He, and mC12-Si are direct-gapsemiconductors with band gaps of 1.13-1.34 eV. Impor-tantly, mC24-Si He has an electric-dipole-transition al-lowed direct band gap, making it a good candidate pho-tovoltaic material.Structure predictions for the Si–He system were per-formed using CALYPSO, which has correctly pre-dicted many stable compounds under high pressure.
The structural optimization and electronic and op-tical properties were calculated using density func-tional theory as implemented in the Vienna ab ini-tio simulation package, adopting the Perdew-Burke-Ernzerhof exchange-correlation functional under the gen-eralized gradient approximation. The Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional was employed tocorrect the electronic band structures. All-electron pro-jector augmented wave pseudopotentials with 1 s and3 s p valence configurations were chosen for He and Siatoms, respectively. A plane wave cutoff energy of 800eV and k-point mesh of 2 π × − were set to en-sure total energy and forces convergence better than 1meV/atom and 1 meV/˚A, respectively. Phonon calcu-lations were carried out using a supercell approach asimplemented in PHONOPY code. First-principles MDsimulations using N (number of particles), V (volume),and T (temperature) were performed at 0 GPa and 300K. × × He (144 atoms)and mC16-Si (96 atoms), and 2 × × He (196 atoms) and mC12-Si (144 atoms) wereemployed. The migration barriers were calculated us-ing the climbing image nudged elastic band (CI-NEB)method based on supercells containing one He atomand 48 host Si atoms for both mC24-Si He and mC16-Si He. VASPKIT was used to resolve the results ofthe transition dipole moment and the optical absorptionspectra (the imaginary part of the dielectric function, ε ). FIG. 3. (a)
Migration pathways of He atoms from site Ato site B along the channels in mC24-Si He and mC16-Si He.The shaded regions indicate the longitudinal section of thechannels. (b)
Energy barriers for He migration along thechannels at zero pressure, as well as Na migration in
Cmcm -Na Si . Structure predictions are first performed for Si He at10 GPa with a maximum of eight formula units (f.u.) in asimulation cell. The previously proposed hP6-Si He issuccessfully predicted, but with much higher enthalpy, asshown in Fig. 1(a). Instead, the energetically most stablestructure for Si He is mC24-Si He, which is monoclinicwith space group C /m (8 f.u. in a unit cell) and is ∼ He. Static-lattice enthalpy calculations reveal that mC24-Si He re-mains energetically most stable up to 17.4 GPa, abovewhich hP6-Si He takes over, see Fig. 2(a). A previ-ous MD simulation suggests that hP6-Si He could beformed at 7 GPa and 1500 K. Therefore, we examine theeffect of temperature on the relative stability of the twostructures using the quasi-harmonic approximation andfind that temperature does not change the phase diagramof Si He, but rather postpones the transition pressure to25 GPa at 1500 K. This result indicates that the newlypredicted mC24-Si He phase is more favorable than hP6-Si He in experimental synthesis at low pressures.In mC24-Si He, each Si atom connects to four otherSi atoms to form three-dimensional networks with bondlengths of 2.43 ˚A. Two kinds of channels sharing edges arefound along the b-axis formed by five- or seven-memberedrings of Si atoms. A zigzag arrangement of He atoms islocated inside the larger channels formed by the seven-membered rings (see Supplemental Material, Fig. S1).The shortest distance between He and the Si channel is2.59 ˚A, which is shorter than the Na–Si distance (3.01 ˚A)in Na Si . Similar host-guest structures have been re- ported in several other compounds, such as Na Si andHeN . The previously proposed hP6-Si He can alsobe regarded as a host-guest structure with a distorted di-amond hexagonal host Si lattice encapsulating guest Heatoms inside the hexagonal channels. The lower enthalpyof mC24-Si He compared with hP6-Si He suggests thatSi can form larger channels for the incorporation of He.
FIG. 4. Electronic band structures of (a) mC24-Si He, (b) mC16-Si He, (c) mC16-Si and (d) mC12-Si at 0 GPacalculated based on the HSE06 functional. Red solid andblue hollow circles represent the valence band maximum andconduction band minimum, respectively. The lower panels ineach figure are the square of the transition dipole moment. To search for other possible stable Si–He compounds,structural predictions are also performed for Si x He y ( x = 1–12 and y = 1–4) at 10 GPa using a maximum of40 atoms in a simulation cell. Fig. 2(b) summarizes theformation enthalpies of the stoichiometries with respectto decomposition into mC24-Si He and CD-Si. Surpris-ingly, a new stable compound with stoichiometry Si Heis identified with a negative formation enthalpy. The en-ergetically most stable structure is mC16-Si He, which ismonoclinic with space group C /m (4 f.u. in a unit cell),as shown in Fig. 1(b). mC16-Si He shares similar struc-tural motifs with mC24-Si He, having a host-guest struc-ture with Si-channels filled with He atoms. Nearly iden-tical channels formed by five-membered rings of Si areobserved in both mC16-Si He and mC24-Si He. mC16-Si He has a higher ratio of Si than mC24-Si He, whichleads to larger channels formed by eight-membered Sirings enclosing He zigzag chains with a Si-He distance of2.81 ˚A. The dynamic stability of mC24-Si He and mC16-Si He at 10 and 0 GPa is confirmed by phonon disper-sion calculations. The MD simulation reveals that bothcompounds exhibit thermodynamic stability at ambientpressure and temperature (300 K), suggesting that bothcould be quenched and recovered at ambient conditionsonce formed (see Figs. S2 and S3).
E n e r g y ( e V )
Absorption ( e A M 1 . 5 C D - S i m C 1 6 - S i m C 2 4 - S i H e
FIG. 5. Imaginary part of the dielectric functions of variousSiHe compounds and Si allotropes calculated with the HSE06functional, as well as the reference air mass 1.5 (AM1.5) solarspectral irradiance. The inset shows a zoom in energy rangeof 0.8–2.0 eV for clarity.
Electron localization function calculations exclude theexistence of Si–He covalent bonds in both compoundsgiven the absence of electron localization between them(see Fig. S4). Bader charge analysis suggests slightcharge transfer from the Si framework to each He atomof 0.05 electrons in mC24-Si He and 0.04 electrons inmC16-Si He, similar to those predicted in Na He andFeO He. The weak interaction between the Si frame-works and He atoms indicates the possible removal of Hefrom the structures. Therefore, we examine the energybarriers of He diffusing along the channels, see Fig. 3(a).CI-NEB calculates energy barriers of 0.37 and 0.18 eVfor mC24-Si He and mC16-Si He, respectively. Thesebarriers are much lower than that (0.75 eV) faced whenremoving Na from Cmcm-Na Si , see Fig. 3(b), in-dicating comparatively easy removal of He atoms frommC24-Si He and mC16-Si He.Figs. 3(c) and (d) show two pure Si structures obtainedby removing He from mC24-Si He and mC16-Si He, de-noted as mC16-Si and mC12-Si, respectively. Both Siallotropes retain Si frameworks nearly identical to thoseof the corresponding compounds. Phonon dispersion andMD calculations confirm the stability of both allotropes(see Figs. S2 and S3). A literature survey surprisinglyfound that the two Si structures have been previouslypredicted with much higher energies ( ∼
80 meV) thanCD-Si.
Metastable structures with higher energiesare generally difficult to synthesize directly. Here, weprovide a potential chemical pathway for the synthesisthese two metastable Si allotropes, namely removing Heatoms from pressure-stabilized SiHe compounds by ther-mal degassing.Photovoltaic materials require a suitable direct bandgap to ensure a large overlap with the solar spectrumin the visible range, and thus strong solar absorption.Electronic structures calculated on basis of the HSE06functional reveal that both mC24-Si He and mC16-Si Hehave direct band gaps of 1.34 and 1.28 eV, respectively, close to the ShockleyQueisser limit (1.34 eV). Interest-ingly, after the removal of He atoms, mC12-Si retains adirect gap, although it is slightly decreased to 1.13 eV.In contrast, mC16-Si gains a quasi-direct gap with di-rect band gap of 1.12 eV at the Γ point, which is slightlylarger than the indirect band gap of 0.84 eV located be-tween the Γ and M points. The retained direct bandgap in mC12-Si suggests a weak interaction between Heand the Si channels in mC16-Si He, which is verified bythe tiny charge transfer (0.04 eV) between them, as wellas the negligible volume collapse (3%) after removal ofthe He atoms. Compared with mC16-Si He, the removalof He from mC24-Si He distinctly changes the Si frame-work, which undergoes a 7% volume collapse and localdeformation (see Table S2), resulting in an indirect bandgap in mC16-Si.A direct band gap does not in itself guarantee goodabsorption, there should also be a dipole-allowed directtransition. Therefore, further calculation of the squareof the transition dipole moment ( P ) explores the tran-sition permissibility between the direct band gaps. In-terestingly, mC24-Si He shows a dipole-allowed directtransition with large P value at the Γ point, suggest-ing good potential as a photovoltaic material. The in-direct band gap in mC16-Si is dipole-forbidden, but thelarge P value related to the direct band gap at the Γpoint provides the possibility of good absorption. Incontrast, mC16-Si He, mC12-Si, and the previously pro-posed hP6-Si He exhibit a dipole-forbidden direct bandgap in view of the corresponding zero P value, excludingthem as good photovoltaic absorbers. Fig. 5 comparesthe calculated imaginary parts of the dielectric constantof mC24-Si He, mC16-Si and CD-Si. Optical absorptionin mC24-Si He starts at ∼ He and mC16-Si have much better solarabsorption capacities than CD-Si, as indicated by theirbroader overlap with the AM1.5 solar spectrum. He, which has two electrons, is the most chemically in-ert natural element, although several recent works havepredicted or synthesized He-containing compounds.
Despite this, He can be regarded as chemically inert inSi-He, as the atoms are almost completely independent ofthe surrounding structure with negligible charge gainedfrom Si. Nonetheless, the current results provide evi-dence that the incorporation of He helps to stabilize newSi frameworks with weak van der Waals interactions. Heappears to be chemically inert in all its known com-pounds (e.g. Na He and HeN ), allowing it to beremoved easily from the surrounding structure withoutchanging the structure substantially. Importantly, theremoval of He hardly alters the charge distribution ofthe Si framework owing to the negligible charge transfer,allowing the electronic structures to be retained after Heremoval. This is confirmed by the direct band gap beingretained in mC12-Si formed from mC16-Si He. There-fore, He appears to be a good intermediate for designingnew functional materials.In conclusion, extensive structure searches of Si–Hesystems predicted two dynamically stable compounds(mC24-Si He and mC16-Si He) with open frameworkstructures comprising Si channels containing zigzag ar-rangements of He atoms. CI-NEB calculations revealedthat the He could be easily removed along the channelsin mC24-Si He and mC16-Si He to leave the pure Si al-lotropes, mC16-Si and mC12-Si, respectively. There weredirect band gaps found in the electronic structures ofmC24-Si He, mC16-Si He, and mC12-Si, whereas mC16-Si showed a quasi-direct band gap. The dipole-alloweddirect band gap of 1.34 eV in mC24-Si He makes it apotential thin-film photovoltaic material. 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