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Si : A sp Silicon Allotrope with Spirally Connected Si Tetrahedrons Kun Luo, Zhisheng Zhao, Mengdong Ma, Shuangshuang Zhang, Xiaohong Yuan, Guoying Gao, xiang-feng zhou, Julong He, Dongli Yu, Zhongyuan Liu, Bo Xu, and Yongjun Tian Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.6b02484 • Publication Date (Web): 07 Sep 2016 Downloaded from http://pubs.acs.org on September 7, 2016
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Chemistry of Materials
Si10: A sp3 Silicon Allotrope with Spirally Connected Si5 Tetrahedrons Kun Luo,† Zhisheng Zhao,*,† Mengdong Ma,† Shuangshuang Zhang,† Xiaohong Yuan,† Guoying Gao,† Xiang-Feng Zhou,‡ Julong He,† Dongli Yu,† Zhongyuan Liu,† Bo Xu,*,† and Yongjun Tian† † State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004, China ‡ School of Physics and Key Laboratory of Weak-Light Nonlinear Photonics, Nankai University, Tianjin 300071, China ABSTRACT: Silicon as a fundamental semiconductor material plays an essential role in modern electronics industry. Exploring new silicon allotropes with structural and electronic properties distinct from those of the diamond-structured Si has been a long-pursued objective. Here, an orthorhombic structure with ten Si atoms in the unit cell (space group Pnnn), Si10, is revealed from first-principles structural search. This structure, with an indirect bandgap of 1.01 eV, is assembled by spirally connected Si5 tetrahedrons. The simulated d-spacings and diffraction angles between different crystal planes of Si10 match those of an entirely new and structural unsolved metastable silicon phase synthesized recently with an ultrafast laser-induced confined microexplosion method. Further analysis suggests that Si10 may originate from the assembly of Si5 clusters probably produced by a radiation-induced disintegration of SiO2 initially used as a confined cover above the Si surface.
Silicon is the second most abundant element in the earth’s crust and has been widely used for vital components in modern electronic devices. Due to the ability of silicon to adopt sp2- and sp3-hybridized states, a variety of Si allotropes other than the common Si with a cubic diamond structure have been synthesized at ambient conditions showing rich electronic and optical behaviors, such as Si nanotubes, Si clathrates, allo-Si, and silicene.1–10 Under pressure, more attractive Si phases can be produced through pressure-induced phase transitions. For example, dense metallic silicon phases with high coordination number can be obtained through following phase transitions: cubic diamond (Si-I) → -Sn (Si-II) at 12 GPa → orthorhombic Imma phase (Si-XI) → simple hexagonal sh (Si-V) at 1316 GPa → orthorhombic Cmca phase (Si-VI) at 38 GPa → hexagonal close pack hcp (Si-VII) at 42 GPa → face-centered cubic fcc (Si-X) at 78 GPa.11–13 The formation of rich Si polytypes is essentially originated from the pressure-induced deformation, breakage, and restructuring of weak Si-Si bonds. The aforementioned transitions are not fully reversible upon pressure release where kinetics factors rather than thermodynamics ones play a key role. Some metastable Si phases can be recovered to ambient pressure by depressurizing metallic high-pressure phases with different release rates. For example, bc8 (Si-III) and r8 (Si-XII) phases were obtained at a slow pressure release rate of ca. 10-3 GPa/s,14,15 and Si-VIII and Si-IX with heretofore unresolved structures had been reported after rapid decompression with rates of 102-104 GPa/s.16 Recently, under ultrahigh depressurization
and temperature quenching rates (1011 GPa/s and 1010 K/s, respectively), more new metastable Si phases were recovered through ultrafast laser-induced confined microexplosion.17 These quenchable metastable Si phases are expected to possess variable electronic features ranging from semiconducting, semi-metallic/metallic, to even superconducting.17–19 Due to the adverse reality from structural complexity, phase content and purity, it is extremely difficult to fully resolve the crystal structures of recovered Si allotropes experimentally with sole diffraction methods. Theoretical considerations, i.e., structure search methods combined with first-principles calculations, provide crucial helps in identifying these structure-unknown phases, such as the T12 structure proposed for Si-XIII,20 Ibam, P42/m, and P-4 structures for tetragonal Si-IX phase.21,22 To account for the electron diffraction patterns of multiple Si phases produced by laser-induced confined microexplosion, bt8, st12, t32 and t32* structures of Si were proposed.17–19,23 However, some interplanar spacings remain unexplained in the diffraction patterns, indicating the presence of more unresolved phase.17 Here, we propose a new Si allotrope with an orthorhombic structure, Si10 (10 atoms per unit cell), from ab initio particle swarm structure search. Si10 shows thermodynamic stability comparable to most of the experimentally known or theoretically predicted sp3 Si. The simulated electron diffraction patterns of Si10 match some unexplained reflections of the unidentified Si phases from laser-induced con-
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We explored the energy landscape of Si allotropes at ambient and high pressures with cell sizes up to 16 atoms through CALYPSO search,24,25 which was unbiased by any known structure and had been proved to be highly effective for predicting new structures.26 Only structures with enthalpies similar to known metastable phases of Si were further considered. The subsequent structural optimizations and property predictions were performed based on the density functional theory (DFT) as implemented in the CASTEP code,27 in which the Vanderbilt ultrasoft pseudopotential was used.28 The electron−electron exchange interaction was described using the Ceperley-Alder exchange-correlation function parameterized by Perdew and Zunger (CA–PZ) within the local density approximation (LDA).29,30 A k-point sampling of 0.04 2 Å -1 and a planewave cutoff of 400 eV were used. The dynamic stability of the structure was verified by the phonon spectrum calculation through the linear response method.31,32 The elastic moduli and electron diffraction pattern of the investigated Si structures were also calculated. To obtain the accurate electronic band structure, imaginary part of dielectric function, and the absorption spectrum, the Heyd-ScuseriaErnzerhof (HSE) hybrid functional was used.33,34 The selected calculation parameters were all tested to ensure energy convergence less than 1 meV per atom. See Supporting Information (SI) for more calculation details. 98.1
This structure is fully sp3-hybridized, and composed of twisted five-membered rings connected in a chain-like manner. The appearance of five-membered rings in Si is not surprising, which is the basic building unit in the known open-framework silicon allotropes such as silicon clathrate,1,2,5,6,8 allo-Si,4 and Si24.10 At first glance, Si10 looks similar to the T12 structure previously proposed for SiXIII,20 but with two atoms fewer in the conventional unit cell. S10 can also be considered as composed of Si5 tetrahedrons interlinked through bridge bonds (Figure 1b, and 1c). The Si5 tetrahedron has four vertex atoms bonded to a central one, and has a configuration similar to that of Si5 cluster evidenced in oxygen-vacancy defects (E’) generated at buried SiO2.35,36 The difference is that the Si5 cluster in Si10 shows a squashed tetrahedral configuration (bond length of 2.352 Å close to that of Si-I, three unequal bond angles of 98.1°, 100.7°, and 132.3°). The density of Si10 is 2.66 g/cm3 at ambient pressure, obviously higher than that of Si-I and comparable to those of the high-pressure quenched dense Si phases, such as bc8, st12, r8, and bt8.14,15,18,19 0.20
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fined microexplosion.17 The analysis of the structure transmissibility suggests this metastable Si polymorph may originate from the laser-induced disintegration of SiO2 layer.
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8
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Figure 2. a) Calculated enthalpies of various Si allotropes relative to Si-I as a function of pressure. b) Phonon dispersion curve of Si10 at ambient pressure.
Figure 1. Crystal structure of Si10: a) 3D view of conventional cell; b) Two representations of a D2d-symmetric Si5 cluster; c) An illustration of the body-centered-orthorhombic Si10 composed of two type of differently orientated Si5 clusters (shadowed with different colors) spirally connected. The Si10 structure adopts a Pnnn space group (No. 48) and contains 10 atoms/cell, wherein atoms occupy the 2a (0.5, 0.5, 0.5) and 8m (0.252, 0.846, 0.647) positions. At ambient pressure, the optimized lattice parameters are a = 3.830 Å , b = 4.343 Å , and c = 10.516 Å .
The search for low-energy structures with 2, 4, 6..., and 16 atoms/cell was conducted under the pressure conditions of 0, 5, 10 GPa, respectively. In addition to some previously discovered Si structures, we found a new dense orthorhombic Si10 phase with 10 atoms per unit cell (Figure 1a).
To check the thermodynamic stability, the enthalpies of Si10 under pressure were calculated and compared with those of the experimentally known or theoretically predicated Si phases, such as bc8, st12, r8, bt8, t32, t32*, m32, m32*, and Ibam structures.14,15,17–19,21,23 As demonstrated in Figure 2a, these structures are all pressure-driven with respect to Si-I, i.e., high pressure favors these metastable phases. At pressure lower than 4 GPa, these metastable phases have very close enthalpies which sit between those of Si-I and high pressure Si-II phase. Si-II has a lower enthalpy than those of other metastable phases at pressure higher than ca. 6 GPa, and further becomes the most stable phase at pressure higher than 7.5 GPa. This indicates that these metastable phases are hard to be obtained by taking into account of the thermodynamic factor alone. Several metastable phases of Si including bc8, r8, st12, and bt8 phases were experimentally recovered from the high-pressure Si-II with different decompression rates,14,15,17 indicating the kinetic factor plays a key role in the reverse transi-
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tion of high-pressure metallic Si phase during the decompression. Moreover, these metastable Si phases might also be obtained from Si-I with rapid compressing rates.
a)
We further studied the elastic moduli of Si10 in the linear elastic strain range (see Supplementary Table 1). The elastic constants of Si10 satisfy the generalized elastic stability criteria for the orthorhombic crystal. The criteria is given as follows: C11 > 0, C44 > 0, C55 > 0, C66 > 0, C11C22 > (C12)2, and C11C22C33 + 2C12C13C23 − C11(C23)2 − C22(C13)2 − C33(C12)2 > 0.37–39 Si10 has bulk modulus (97 GPa) and shear modulus (68 GPa) similar to those of Si-I. Furthermore, the calculated ground-state phonon dispersion curve of Si10 (Figure 2b) shows no imaginary phonon frequency in the whole Brillouin zone, indicating the dynamic stability of Si10 at ambient condition. These results confirm that Si10 is metastable and may be recoverable once formed. The electronic property of Si10 were also investigated. To obtain the accurate bandgap, we used the HSE06 functional33,34 to calculate the band structures and density of states (DOS) of Si10 at ambient pressure (Figure 3). Si10 has an indirect gap of 1.01 eV, which is slightly smaller than that of Si-I (1.17 eV). Note the direct band gap of Si10 (1.37 eV) at the G point is less than half that of Si-I (3.4 eV). Since more than 90% of solar light falls in the visible and infrared region, the smaller direct band gap of Si10 would benefit the absorption of low-energy photons.10,26,40–42 The optical properties of Si10 and Si-I were also calculated employing the HSE06 functional (Supplementary Figure 1). Si10 starts to absorb the sunlight at lower energy than that of Si-I, indicating its great potential in solar cell applications.
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-6
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T Y
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Figure 3. Band structure and DOS of Si10 at ambient pressure.
For practical reasons, it is essential to investigate the possibility of experimental synthesis of the predicted structures. Here we argue that Si10 may have been produced during the ultrafast laser-induced confined microexplosion.17 In this experiment, several Si allotropes were identified based on the analysis of the selected area electron diffraction (SAED) patterns of the final product.17 However, there are still some diffraction spots remaining unexplained. In Supplementary Table 2, the experimentally determined dspacings17 are compared with the calculated ones from previously proposed Si metastable phases (bt8, st12, t32, t32*) and Si10. The d-spacings of 14 crystallographic planes of Si10
Figure 4. Simulated electron diffraction patterns of Si10 phase compared with the experimental data.17 a) Diffraction spots (red circles) from the simulated SAED pattern taken along [100] zone axis. b) Diffraction spots (red circles) from the simulated SAED pattern taken along [010] zone axis. The overlapped simulated and experimental spots indicate the perfect matching of d-spacings as well as the diffraction angle relationships between different crystal planes. The pink triangles, green squares, and green circles correspond to Si-VIII, t32-Si, and t32*-Si, respectively.17
match the experimentally observed values nicely. Moreover, 6 out of 11 unsolved d-spacings in the experiment can be accounted for by those of Si10 (10.80, 3.70, 3.45, 3.18, 2.96, and 1.97 Å ), supporting the existence of Si10 phase in the final product. To provide a stronger evidence, we simulated the single-crystal diffraction patterns of Si10 phase and compared it with the experimental ones. As shown in Figure 4a, the diffraction spots (red circles) from the simulated SAED pattern taken along [100] zone axis overlaps
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some of the experimentally observed and unexplained spots remarkably well. The same situation occurs in Figure 4b where the zone axis is along [010] direction. See Supplementary Figure 2 and 3 for more comparisons between simulated electron diffraction patterns of Si10 phase and the experimental ones. This kind of overlapping indicates that, in addition to the d-spacings matching, the reflections of predicted phase (i.e., Si10) satisfy the diffraction angle relationship between different crystal planes, providing a strong evidence of the experimental presence of Si10. The formation of metastable Si phases is generally attributed to the kinetically controlled reverse-transformation of the high-pressure metallic Si phases with density higher than Si-I or even Si-II phase during decompression, as previously reported.14,15,17,18 Although the possible transition paths from Si-II to bc8, r8, bt8, st12, and t32 have been reported,18,23 it is hard to find the corresponding structural relationship between Si-II (or the metallic phases with higher density) and the structurally complicated metastable phases such as m32, m32*, and t32*.17 In the ultrafast laser-induced confined microexplosion experiment, a powerful ultrashort focused laser pulse was used to generate a microexplosion at the interface between a transparent amorphous SiO2 layer and an opaque crystalline Si substrate.17 We thus speculate an alternative pathway to form metastable Si phases during this microexplosion experiment: some new Si phases, specifically S10, may result from the disintegration of plasma-state silica rather than phase transition of silicon. Our speculation is based on the following points: First, the ultrahigh temperature generated by laser irradiation can lead to the breaking of some Si−O bonds.43 A similar case, the observation of superdense aluminum, occurred when α-Al2O3 was irradiated by laser.44 The appearance of voids at the Si/SiO2 interface after microexplosion17 also indicates the oxygen dissociation from the SiO2. Second, previous studies indicated the existence of small Si5 clusters in the oxygen-vacancy defects generated at the surface of buried SiO2.35,36 In addition, Si10 is energetically more favorable than Si5 clusters. Considering the lower energy of Si10 and the structural relationship between Si10 and Si5 clusters, it is highly possible that the Si10 was formed by direct assembly of Si5 clusters. Last, note that only metastable r8 and bc8 phases as well as Si-VIII phase were produced when laser pulses focused at the freestanding silicon surface without the involvement of silica.45–47 Therefore, Si10 phase is highly likely to be formed by the disintegration of plasma-state silica rather than phase transition of silicon in the microexplosion experiment.17 This finding may bring new insights about the formation of metastable Si allotropes during the microexplosion experiment, and give a direction to quest for new Ge phases with similar synthetic process. In summary, a new Si allotrope, Si10, has been theoretically designed through the first-principles structural search. Si10 shows thermodynamic stability comparable to other Si metastable phases, and may be kinetically formed from the assembly of Si5 clusters. The d-spacings and diffraction angle relationships of Si10 match those of the structural unsolved metastable silicon phase recently synthe-
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sized by an ultrafast laser-induced confined microexplosion, indicating the viability to achieve Si10. The current study may enrich the common understanding of silicon high-pressure transitions, and provides an alternative and significant pathway to achieve novel Si metastable phases through disintegration and assembly.
ASSOCIATED CONTENT Supporting Information. The calculation details; mechanical and optical properties of Si10 and Si-I; comparison of the calculated d-spacings of Si10 with the observed values in the experiment; simulated electron diffraction data of Si10; and the simulated electron diffraction patterns of Si10 phase compared with the experimental data are clearly shown in Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org.
AUTHOR INFORMATION Corresponding Author * Z. Zhao. E-mail:
[email protected]; * B. Xu. E-mail:
[email protected] Notes The authors declare no competing financial interests.
ACKNOWLEDGMENT This work was supported by NSFC (Grants Nos. 51525205, 51421091, 51332005, and 51272227), NBRPC (Grant No. 2011CB808205) and NSF for Distinguished Young Scholars of Hebei Province of China (Grant No. E2014203150).
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Chemistry of Materials
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TOC Graphic Laser
O2
Plasma expansion
Assembled
Si5 cluster Silica
Transition state of Si
ACS Paragon Plus Environment
Si10
