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Prediction of Novel Phase of Silicon and Si–Ge Alloys Journal of Solid State Chemistry 233 (2016) 471–483 Contents lists available at ScienceDirect Journal of Solid State Chemistry journal homepage: www.elsevier.com/locate/jssc Prediction of novel phase of silicon and Si–Ge alloys Qingyang Fan a, Changchun Chai a, Qun Wei b,n, Yintang Yang a, Qi Yang a, Pengyuan Chen a, Mengjiang Xing c, Junqin Zhang a, Ronghui Yao b a Key Laboratory of Ministry of Education for Wide Band-Gap Semiconductor Materials and Devices, School of Microelectronics, Xidian University, Xi'an 710071, PR China b School of Physics and Optoelectronic Engineering, Xidian University, Xi'an 710071, PR China c Faculty of Information Engineering & Automation, Kunming University of Science and Technology, Kunming 650051, PR China article info abstract Article history: The structural, thermodynamic, elastic, anisotropic and electronic properties of P2221-Si have been Received 21 August 2015 studied using first-principles calculations. The elastic constants are satisfied with mechanical stability Received in revised form criteria. The mechanical anisotropy is predicted by anisotropic constants Poisson's ratio, shear modulus, 5 November 2015 Young's modulus and three dimensional curved surface of Young's modulus. These results show that Accepted 13 November 2015 P222 -Si and Si–Ge alloys are anisotropic. The sound velocities in different directions and Debye tem- Available online 1 December 2015 1 perature for P2221-Si and Si–Ge alloys are also predicted. Electronic structure study shows that P2221-Si Keywords: is an indirect semiconductor with band gap of 0.90 eV. In addition, the band structures of Si–Ge alloys are Silicon investigated in this paper. Finally, we also calculate the thermodynamics properties and obtained the Si–Ge alloys relationships between thermal parameters and temperature. Mechanical properties & 2015 Elsevier Inc. All rights reserved. Electronic properties 1. Introduction calculations. They found that the band structures of bct and M4 phases of silicon show that they are semiconductors with an in- Silicon is an indispensable material for the modern industry direct band gap, which is twice smaller than that calculated for the because it has lots of unique physical and chemical characteristics. cubic silicon (Si-I, space group: Fd-3m). Utilizing first-principles For example, its excellent electronic and optical properties make it calculations, Hao et al. [14] studied the electronic and elastic an important optoelectronic material [1,2]; its desirable piezo- properties and mechanical properties of a new silicon allotrope resistance coefficients make it almost a perfect material for mi- (T12-Si) to enrich the relevant information. The results show that croelectro-mechanical transducers [3–5]. Many other crystal forms the T12-Si is mechanically anisotropic and has a lower bulk mod- of silicon under pressure have also been reported [6]. The crystal ulus and shear modulus than Si-I. Its hardness is 10.3 GPa, smaller structures of silicon and germanium were studied by energy dis- than that of Si-I (13.5 GPa). Analyses of the electronic properties persive X-ray diffraction at room temperature and pressures up to reveal that T12-Si is an indirect band gap crystal with a gap value of 50 GPa [7]. Silicon transforms to a primitive hexagonal (Si-V) 0.69 eV. Recently, six metastable allotropes of silicon with direct or – structure about 16 GPa, to an others phases Si-VI between 35 and quasidirect band gaps of 0.3 91.25 eV are predicted utilizing ab 40 GPa, and to hcp (Si-VII) about 40 GPa. A transition to the β-Sn initio calculations at ambient pressure by Wang et al. [15]. Five of them possess band gaps within the optimal range for high con- phase initiates at 11.270.2 GPa and two new phases coexist to verting efficiency from solar energy to electric power and also 12.570.2 GPa [8]. To extend the functionality of silicon in appli- have better optical properties than the Si-I phase. De and Pryor cations, a wide range of nanostructures, for instances, nanotubes [16] calculated the electronic band structure and dielectric func- [9], nanowires [10], nanorods [11], and nanoribbons [12],have tions for silicon in lonsdaleite phase and this phase has an indirect been prompted by the modern technology. Wu et al. [13] in- band gap of 0.95 eV. They also calculate the optical properties of vestigated the stabilities and electronic properties of two hy- silicon in the lonsdaleite phase using a transferable model em- pothetical allotropes of silicon, the body-centered tetragonal (bct) pirical pseudopotential method with spin–orbit interactions. and monoclinic (M4) phases utilizing density functional In this paper, a novel silicon phase (space group: P2221) P2221- Si with indirect band gap 0.90 eV is investigated. The original n Corresponding author. structure of P2221 Si is P2221-carbon in Refs. [17,18], with Si E-mail address: [email protected] (Q. Wei). substituting C. Furthermore, the detailed physical properties (such http://dx.doi.org/10.1016/j.jssc.2015.11.021 0022-4596/& 2015 Elsevier Inc. All rights reserved. 472 Q. Fan et al. / Journal of Solid State Chemistry 233 (2016) 471–483 Fig. 1. Unit cell crystal structures of P2221-silicon and Si–Ge alloys. as structural properties, elastic properties, anisotropic and elec- Eruzerhof (PBE) [19],WuandCohen(WC)[20],PBEsol[21] and local tronic properties) of novel silicon allotropes are studied. In addi- density approximation (LDA) functional [22,23] form were adopted tion, the electronic and elastic properties of Si–Ge alloys in P2221 as the exchange and correlation interaction. The properties of the phase are also investigated in this paper. predicted P2221 phases were obtained via ultrasoft pseudopotentials [24] through the CASTEP code [25]. The spacing in the k-point Monkhorst-Pack grid was 0.03 ÅÀ1 (7 Â 3 Â 7) for Brillouin zone sampling [26]. The Broyden–Fletcher–Goldfarb–Shanno (BFGS) [27] 2. Calculated method minimization was used for the convergence criterion. Structural op- A plane-wave basis set with the energy cutoff of 340 eV was used. timization was performed until the enthalpy change per atom was À6 Generalized gradient approximation (GGA) within Perdew–Burke– less than 1 Â 10 eV, the ionic forces on atoms were less than Q. Fan et al. / Journal of Solid State Chemistry 233 (2016) 471–483 473 Table 1 Calculated lattice parameters of P2221-Si and Si-I (in units of Å). P2221 Lattice constants WC PBE PBEsol CA-PZ xa(Å) b (Å) c (Å) a (Å) b (Å) c (Å) a (Å) b (Å) c (Å) a (Å) b (Å) c (Å) 0 5.439 12.988 5.323 5.448 13.017 5.339 5.445 12.995 5.327 5.364 12.803 5.248 0.056 5.453 13.015 5.336 5.461 13.046 5.353 5.458 13.022 5.340 5.372 12.820 5.255 0.111 5.465 13.053 5.350 5.473 13.085 5.367 5.470 13.061 5.355 5.378 12.847 5.265 0.167 5.474 13.098 5.364 5.484 13.129 5.382 5.480 13.105 5.368 5.384 12.873 5.273 0.222 5.486 13.139 5.379 5.494 13.175 5.398 5.491 13.146 5.383 5.391 12.899 5.283 0.278 5.494 13.188 5.394 5.505 13.222 5.412 5.501 13.194 5.398 5.398 12.926 5.292 Fd-3m 5.460 5.465 5.466 5.374 5.402a 5.392a 5.429b 5.465c Exp. 5.431 a Ref. [14]. b Ref. [46]. c Ref. [13]. 1.00 1.00 0.98 0.99 0.96 0.98 0.94 0.97 0.92 0 0 V X / 0.90 / X V 0.96 0.88 0.95 0.86 0 K 0.84 0.94 a/a 200 K 0 300 K b/b 0 400 K 0.82 c/c 0 600 K 0.93 0 3 6 9 1215180 2 4 6 8 1012141618 Pressure (GPa) Pressure (GPa) Fig. 2. The lattice constants a/a0, b/b0, c/c0 compression as functions of pressure and temperature for P2221-silicon. 0.01 eV/Å, and the stress components were less than 0.02 GPa. The found in the silicon allotropes system. The crystal structure of thermodynamic properties of P2221-Si are calculated by the quasi- P2221-Si and Si–Ge alloys are shown in Fig. 1.TheSiatomsoccupy harmonic Debye model [28–32]. Utilizing the quasi-harmonic Debye the Wyckoff positions 4e (0.84569, 0.08485, 0.41830), 4e (0.72918, model, one can obtain the thermodynamic properties of P2221-Si at 0.71207, 0.00700), 2b (0.23378, 0.50000, 0.00000), 2 c (0.00000, pressures and temperatures. 0.81164, 0.25000), 2 c (0.00000, 0.38574, 0.25000), 2d (0.50000, 0.59759, 0.25000) and 2d (0.50000, 0.82627, 0.75000) in P2221-Si, respectively. For Si–Ge alloys, the Ge atoms occupy the positions 3. Results and discussion with the minimum energy. Using both GGA and LDA methods, the equilibrium lattice constants are determined by minimizing the total A thermodynamically stable silicon allotrope, orthorhombic-Si, is energy with respect to variation of the cell volume. The structural 474 Q. Fan et al. / Journal of Solid State Chemistry 233 (2016) 471–483 -106.7 c-Si Lonsdaleite Si -106.8 M-Si Cco-Si P222 -Si Z-Si 1 -106.9 P4 /ncm-Si tP16-Si 2 -107.0 -107.1 Enthalpy (eV/atom) -107.2 -107.3 -10 -5 0 5 10 15 20 Pressure (GPa) Fig.
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