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Article

The Mechanical and Electronic Properties of Carbon-Rich Silicon Carbide

by
Qingyang Fan
1,*,
Changchun Chai
1,
Qun Wei
2 and
Yintang Yang
1
1
Key Laboratory of Ministry of Education for Wide Band-Gap Semiconductor Materials and Devices, School of Microelectronics, Xidian University, Xi’an 710071, China
2
School of Physics and Optoelectronic Engineering, Xidian University, Xi’an 710071, China
*
Author to whom correspondence should be addressed.
Materials 2016, 9(5), 333; https://doi.org/10.3390/ma9050333
Submission received: 29 March 2016 / Revised: 25 April 2016 / Accepted: 27 April 2016 / Published: 30 April 2016
(This article belongs to the Special Issue Computational Multiscale Modeling and Simulation in Materials Science)
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Abstract

:
A systematic investigation of structural, mechanical, anisotropic, and electronic properties of SiC2 and SiC4 at ambient pressure using the density functional theory with generalized gradient approximation is reported in this work. Mechanical properties, i.e., the elastic constants and elastic modulus, have been successfully obtained. The anisotropy calculations show that SiC2 and SiC4 are both anisotropic materials. The features in the electronic band structures of SiC2 and SiC4 are analyzed in detail. The biggest difference between SiC2 and SiC4 lies in the universal elastic anisotropy index and band gap. SiC2 has a small universal elastic anisotropy index value of 0.07, while SiC2 has a much larger universal elastic anisotropy index value of 0.21, indicating its considerable anisotropy compared with SiC2. Electronic structures of SiC2 and SiC4 are calculated by using hybrid functional HSE06. The calculated results show that SiC2 is an indirect band gap semiconductor, while SiC4 is a quasi-direct band gap semiconductor.
Keywords:
silicon carbide; mechanical properties; electronic properties
PACS:
62.20.de; 62.20.dq; 71.20.-b

1. Introduction

Silicon carbide has been investigated since 1907, when Captain H. J. Round first found that silicon carbide can be used as a material for making light-emitting diodes and detectors in early radios [1,2]. SiC is a candidate of choice for high-speed, high-temperature, high-power, and high-frequency device applications because of its wonderful physical properties and electronic properties, such as wide bandgaps, high saturated electron drift velocities, high thermal conductivities, and high-breakdown electric fields. Furthermore, SiC is hard, chemically stable, and resistant to radiation damage. In addition to these extraordinary mechanical properties, SiC is also highly resistant to irradiation, which makes this material a first-choice candidate for various nuclear applications, such as a structural material in future fusion reactors [3,4]. SiC has potential applications in weighty bad circumstances due to its high chemical stability with a good resistance to corrosion. Like silicon, as a semiconductor, SiC can also be doped due to its electronic properties. Moreover, SiC is used in high-power and high-temperature devices. The combination of all these mechanical, electrical, and thermal properties makes SiC a highly sought-after material for biosensor applications [5].
Five independent elastic constants of 4H- and 6H-SiC single crystals have been determined via Brillouin scattering [6]. Elastic constants and sound velocities, calculated using first-principles calculations as a function of pressure, were presented for 2H-SiC by Sarasamaker et al. [7]. The stability and mobility of non-dissociated screw dislocations in 2H-, 4H- and 3C-SiC have been investigated using first-principles calculations. For SiC, it has in fact been shown that plasticity properties at low temperatures are mainly due to these extended defects, regarding which, very little is known. Previous optical work [8,9,10,11] on SiC has focused on the 3C and 6H polytypes because only small attention could be paid to other polytypes; however, 50-mm-thin 4H- and 6H-SiC wafers have become commercially available in recent years. The structural stability and electronic properties of the SimCn graphyne-like monolayers with 18-, 18-, 24-graphyne type structures have been systematically studied using a transferable and reliable semi-empirical Hamiltonian by Yan et al. [12]; they found that the flat SiC and SiC9 graphyne-like monolayers have semiconductor properties with an energy gap of 0.96 eV and 0.69 eV, respectively. The slightly buckled Si2C8 graphyne-like monolayer, on the other hand, behaves like a tiny gap material.
The carbon-rich, silicon-rich, and germanium-rich binary compounds have also been investigated by using density functional theory methodology [13,14,15]. Two new phases of Si8C4 and Si4C8 with P42/nm symmetry were proposed by Zhang et al. [15]; both Si8C4 and Si4C8 were proven to be dynamically and mechanically stable. The band structures of Si8C4 and Si4C8 indicate that they are both indirect semiconductors. Moreover, the density functional theory has also been successfully applied to predict the physical and chemical properties of some other binary compound materials, such as Ca-Mg [16], Si-Ge [17,18], and XBi3 (where X = B, Al, Ga, and In) [19].
Using first-principles calculations, two new SiC2 and SiC4 phases of carbon-rich silicon carbide are proposed in this paper. We propose SiC2 (space group: P42nm) and t-SiC4 (space group: P21/m), whose structures are based on t-SiCN [20] and P21/m-carbon [21], with Si substituting for C. In the present work, we will investigate the structural, chemical bonding, elastic, mechanical anisotropy, and electronic properties of SiC2 and SiC4.

2. Materials and Methods

The calculations were performed using density functional theory (DFT) [22,23], within Vanderbilt ultra-soft pseudo-potentials [24], generalized gradient approximation (GGA), in the form of Perdew–Burke–Ernzerhof (PBE) [25], PBEsol [26], and local density approximation (LDA), in the form of Ceperley and Alder data as parameterized by Perdew and Zunger (CA-PZ) [27], as implemented in the Cambridge Serial Total Energy Package (CASTEP) [28] code. C-2s22p2 and Si-3s23p2 were treated as valence electrons. The cut-off energy was selected as 400 eV, and the k-point sampling of the Brillouin zone was constructed using the Monkhorst–Pack scheme [29], with 10 × 10 × 6 and 5 × 12 × 8 grids in primitive cells of SiC2 and SiC4, respectively. The electronic properties of SiC2 and SiC4 were calculated by using the Heyd–Scuseria–Ernzerhof (HSE06) hybrid functional [30]. The equilibrium crystal structures were achieved by utilizing geometry optimization in the Broyden–Fletcher–Goldfarb–Shanno (BFGS) [31] minimization scheme. The self-consistent convergence of the total energy was 5 × 10−6 eV/atom; the maximum force on the atom was 0.01 eV/Å; the maximum ionic displacement was within 5 × 10−4 Å; and the maximum stress was within 0.02 GPa. The phonon spectra of SiC2 and SiC4 required using the linear response approach, called the density functional perturbation theory (DFPT), which is one of the most popular methods for the ab initio calculation of lattice dynamics [32].

3. Results and Discussion

The crystal structures of SiC2 and SiC4 are shown in Figure 1. There are 12 and 10 atoms in a conventional cell of SiC2 and SiC4, respectively. There are twelve atoms in the conventional cell of SiC2, with atomic positions (Fractional coordinates) of C (0.3650, 0.3650, 0.3577) and (0.3650, 0.3650, 0.1342) and Si (0, 0.5, −0.0039); there are ten atoms in the conventional cell of SiC4, with atomic positions (Fractional coordinates) of C (0.4862, 0.25, 0.6069), (0.7057, 0.75, 0.1069), (0.0263, 0.75, 0.4019), and (0.9484, 0.75, 0.0992) and Si (0.3015, 0.75, 0.1714). SiC2 has a tetragonal crystal structure, with the space group of P42nm (No. 102), while SiC4 has a monoclinic crystal structure, with the space group of P21/m (No. 11). The calculated equilibrium lattice parameters of SiC2 and SiC4 are listed in Table 1. At zero pressure, the lattice constants calculated from GGA of SiC2 are a = 4.1968 Å and c = 7.1067 Å, while the lattice parameters of SiC4 are a = 6.7550 Å, b = 2.7629 Å, c = 4.3794 Å, and β = 75.782°. The densities of SiC2 and SiC4 are 2.765 g/cm3 and 3.191 g/cm3, respectively.
In Figure 2, we illustrate the pressure dependence of the equilibrium lattice parameters for SiC2 and SiC4 under pressure from 0 to 10 GPa. For SiC2, it can be easily observed that the compressibility along the a-axis (b-axis) is easier than along the c-axis. For SiC4, the incompressibility of the c-axis is slightly greater than that of the a-axis and b-axis. Figure 2b shows that the incompressibility of SiC4 is slightly greater than that of SiC2. SiC2 has four different bond lengths, namely, C–C bonds are 1.589 Å and 1.603 Å, while C–Si bonds are 1.905 Å and 1.906 Å. SiC4 has five different bond lengths, namely, C–C bonds are 1.562 Å, 1.615 Å and 1.633 Å, while C–Si bonds are 1.865 Å and 1.898 Å. The average C–C and C–Si bonds are 1.592 Å and 1.906 Å, 1.608 Å and 1.882 Å for SiC2 and SiC4, respectively. The C–C and C–Si bonds for diamond and SiC are 1.535 Å and 1.892 Å for comparison, respectively.
The elastic constant is used to describe the mechanical resistance of crystalline materials to externally applied stresses. The calculated elastic constants of SiC2 and SiC4 are shown in Table 2. From Table 2, it is evident that both SiC2 and SiC4 are mechanically stable because the elastic constants can simultaneously satisfy all of Born’s criteria for the mechanical stability of tetragonal and monoclinic symmetry [33,34]. To ensure the stability of SiC2 and SiC4, the phonon spectra are calculated at ambient pressure (0 K and 0 GPa). Figure 3 shows the phonon dispersions of SiC2 and SiC4. There is no imaginary frequency, which means that SiC2 and SiC4 are stable at ambient pressure. The elastic constants and phonon calculation have confirmed that the predicted SiC2 and SiC4 are mechanically and dynamically stable, respectively.
Using the Voigt–Reuss–Hill method [41,42,43], the bulk modulus (B) and shear modulus (G) are estimated [44,45]. Young’s modulus (E) and Poisson’s ratio (ν) are significant elastic parameters of materials; they are calculated using the formula E = 9BG/(3B + G) and v = (3B − 2G)/[2(3B + G)], respectively. The calculated elastic modulus and Poisson’s ratio of SiC2 and SiC4 are also shown in Table 1. For 3C-SiC, the elastic constants and elastic moduli are much closer to the experimental values; thus, we use the results within LDA to compare the big or small values of the elastic modulus. The bulk modulus, shear modulus, and Young’s modulus of SiC4 are greater than those of SiC2. The bulk modulus, shear modulus, and Young’s modulus of SiC2 are close to those of 3C-SiC. The Young’s modulus of SiC4 is much greater than that of 3C-SiC and SiC2. According to Pugh [46], a larger B/G value (B/G > 1.75) for a solid represents ductility, while a smaller B/G value (B/G < 1.75) usually means brittleness. The B/G values of SiC2 and SiC4 are 1.25 and 1.10, respectively. In other words, SiC4 is more brittle than SiC2. Poisson’s ratio is a factor for the degree of directionality of chemical bonds [47], being v = 0.1 for covalent materials and typically v = 0.25 for ionic materials [48]. In SiC2 and SiC4, the Poisson’s ratios are 0.18 and 0.15, respectively, suggesting the complex bond essence in SiC2 and SiC4.
Moreover, the hardness of SiC2 and SiC4 is calculated using Lyakhov and Oganov’s model [34]. The hardness of SiC2 and SiC4 is 33.6 and 44.0 GPa, respectively. These results match well with our previous prediction. Thus, SiC2 is a hard material, and SiC4 is a superhard material, with potential technological and industrial applications. The value of hardness of SiC, calculated using this model, is 29.3 GPa. The hardness of SiC2 and SiC4 is slightly greater than that of SiC because there is no C–C bond in SiC. The calculated and experimental hardness of diamond is 91.2 GPa [49] and 90.0 GPa [50], respectively, for comparison.
Anisotropy is the property of being directionally dependent, as opposed to isotropy, which implies identical properties in all directions. It can be defined as a difference, when measured along different axes, in a material’s physical or mechanical properties. Young’s modulus for all possible directions and the 2D representation of Young’s modulus in the xy, xz, and yz planes for SiC2 and SiC4 are shown in Figure 4a–d, respectively. For an isotropic system, the 3D directional dependence would show a spherical shape, while the deviation degree from the spherical shape reflects the content of anisotropy [51]. The Young’s modulus of SiC2 varies between 332 and 411 GPa; for SiC4, Young’s modulus varies between 476 and 688 GPa. The ratios of Emax and Emin are 1.24 and 1.45 for SiC2 and SiC4, respectively. SiC4 exhibits a larger anisotropy in its Young’s modulus than that of SiC2. Another way of measuring the elastic anisotropy is given by the universal anisotropic index (AU), which is defined as AU = 5GV/GR + BV/BR − 6, where B and G denote the bulk modulus and shear modulus, respectively, and the subscripts V and R represent the Voigt and Reuss approximations, respectively. Moreover, there must be AU greater than or equal to zero; for isotropic materials, AU must be equal to zero. The AU of SiC2 is 0.07, which shows that SiC2 exhibits a smaller anisotropy; for SiC4, the larger AU (0.21) shows a larger anisotropy.
It is well known that the electronic structure determines the fundamental physical and chemical properties of materials. The failure of LDA and GGA to accurately predict the band gaps of semiconducting materials is caused by a functional derivative discontinuity of the exchange–correlation potential, which can be avoided by using the hybrid functional. Thus, we calculate the band structure and density of states (DOS) of SiC2 and SiC4 by using the HSE06 functional, which are illustrated in Figure 5. From Figure 5, we can easily find that SiC2 and SiC4 are semiconductors with a band gap of 0.91 eV and 2.28 eV, respectively. For SiC2, the conduction band minimum (CBM) is at (0.2353 0.2353 0.5000) (Fractional coordinates) along the Z–A direction, while the valence band maximum (VBM) is located at (0.5000 0.5000 0.0714) along the A–M direction (see Figure 5a). For SiC4, CBM is at the D point, while the VBM is located at the G point (see Figure 5b). The direct gap at D is 2.34 eV, which is slightly larger than the indirect gap of 2.28 eV. Thus, SiC4 has a quasi-direct band gap. Figure 6a shows the partial density of state (PDOS) of SiC2; the PDOS is divided into three parts: the first is the energy range from −18 eV to −10 eV, where the contribution from Si-p is very small compared with that of other orbitals, and the main contributions to the upper band are from the C-s orbital. The middle band is in the range from –10 eV to 0 eV; the main contributions in this part are from the C-p orbital and Si-p orbital. The last band has energies above the Fermi level. In the upper band, the contribution from the Si-p orbital is great compared with that of other orbitals for the first place, while for the second, the contribution from the C-p orbital is great. From Figure 6b, we find that the PDOS of SiC4 is similar to that of SiC2. For the energy range from −25 eV to −15 eV, the contribution from C-s is very great compared with that from the other orbitals. For the energy range from −15 eV to 15 eV, the main contribution comes from the C-p and Si-p orbitals.

4. Conclusions

The structural, mechanical, anisotropic, and electronic properties of SiC2 and SiC4 have been investigated for the first time, utilizing first-principle calculations based on density functional theory. The elastic constants and phonon calculations reveal that SiC2 and SiC4 are mechanically and dynamically stable at ambient pressure. Moreover, by analyzing the B/G ratio, SiC2 and SiC4 are naturally brittle. The anisotropic calculations show that SiC2 and SiC4 are anisotropic materials and that SiC4 exhibits a greater anisotropy than SiC2. Finally, the band structure calculations predict that SiC4 is a quasi-direct band gap semiconductor, with a band gap of 2.28 eV, while SiC2 is an indirect band gap semiconductor, with a band gap of 0.91 eV.

Acknowledgments

This work was supported by the Natural Science Foundation of China (No. 61474089) and the Open Fund of Key Laboratory of Complex Electromagnetic Environment, Science and Technology, China Academy of Engineering Physics (No. 2015-0214. XY.K).

Author Contributions

Qingyang Fan and Qun Wei designed the project; Qingyang Fan, Changchun Chai, and Qun Wei performed the calculations; Qingyang Fan, Qun Wei, and Yintang Yang determined the results; Qingyang Fan and Changchun Chai wrote the manuscript.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Unit cell crystal structures of SiC2 (a) and SiC4 (b).
Figure 1. Unit cell crystal structures of SiC2 (a) and SiC4 (b).
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Materials 09 00333 g002 1024
Figure 2. The compression lattice constants a/a0, b/b0, c/c0 as functions of pressure SiC2 (a) and SiC4 (b).
Figure 2. The compression lattice constants a/a0, b/b0, c/c0 as functions of pressure SiC2 (a) and SiC4 (b).
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Materials 09 00333 g003 1024
Figure 3. Phonon spectra for SiC2 (a) and SiC4 (b).
Figure 3. Phonon spectra for SiC2 (a) and SiC4 (b).
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Materials 09 00333 g004 1024
Figure 4. The directional dependence of Young’s modulus for SiC2 (a) and SiC4 (c); 2D representation of Young’s modulus in the xy plane, xz plane, and yz plane for SiC2 (b) and SiC4 (d).
Figure 4. The directional dependence of Young’s modulus for SiC2 (a) and SiC4 (c); 2D representation of Young’s modulus in the xy plane, xz plane, and yz plane for SiC2 (b) and SiC4 (d).
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Materials 09 00333 g005 1024
Figure 5. Electronic band structures of SiC2 (a) and SiC4 (b). The red and blue points indicate the conduction band minimum and valence band maximum, respectively.
Figure 5. Electronic band structures of SiC2 (a) and SiC4 (b). The red and blue points indicate the conduction band minimum and valence band maximum, respectively.
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Materials 09 00333 g006a 1024Materials 09 00333 g006b 1024
Figure 6. The partial density of states of SiC2 (a) and SiC4 (b).
Figure 6. The partial density of states of SiC2 (a) and SiC4 (b).
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Table
Table 1. The calculated lattice parameters and elastic moduli of SiC2, SiC4, and 3C-SiC. (Space group: SG).
Table 1. The calculated lattice parameters and elastic moduli of SiC2, SiC4, and 3C-SiC. (Space group: SG).
MaterialsSGMethodsabCβBGEv
SiC2P42nmPBE 14.197 7.107 2031623840.18
PBEsol 14.193 7.100 2051724030.17
CA-PZ 14.141 7.010 2171784190.18
SiC4P21/mPBE 16.7552.7634.37975.782852585950.15
PBEsol 16.7442.7494.36975.752302545570.10
CA-PZ 16.7522.7624.37875.812502746020.10
SiCF-43mPBE 14.348 2171874360.17
PBEsol 14.362 2161864330.17
CA-PZ 14.300 2292004650.16
PBE 24.380 235 5
PBE 34.344 224 6
Exp. 44.360 227 71924480.17
1 This work, 2 Ref [10], 3 Ref [35], 4 Ref [36], 5 Ref [37], 6 Ref [38], 7 Ref [39].
Table
Table 2. The calculated elastic constants of SiC2, SiC4, and 3C-SiC.
Table 2. The calculated elastic constants of SiC2, SiC4, and 3C-SiC.
MaterialsMethodsC11C22C33C44C55C66C12C13C23C15C25C35C46
SiC2PBE 1373 447172 18194114
PBEsol 1398 449186 177103100
CA-PZ 1409 483191 191101115
SiC4PBE 16066506483162801965818887−7−9−22−19
PBEsol 15765606192902851876511742−163−6−11
CA-PZ 16096126773133052035912154−23−1−8−15
SiCPBE 1385 243 132
PBEsol 1381 244 133
CA-PZ 1408 261 140
PBE 2382 239 128
CA-PZ 3390 253 134
Exp. 4390 256 142
1 This work, 2 Ref [10], 3 Ref [36], 4 Ref [40].

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Fan, Q.; Chai, C.; Wei, Q.; Yang, Y. The Mechanical and Electronic Properties of Carbon-Rich Silicon Carbide. Materials 2016, 9, 333. https://doi.org/10.3390/ma9050333

AMA Style

Fan Q, Chai C, Wei Q, Yang Y. The Mechanical and Electronic Properties of Carbon-Rich Silicon Carbide. Materials. 2016; 9(5):333. https://doi.org/10.3390/ma9050333

Chicago/Turabian Style

Fan, Qingyang, Changchun Chai, Qun Wei, and Yintang Yang. 2016. "The Mechanical and Electronic Properties of Carbon-Rich Silicon Carbide" Materials 9, no. 5: 333. https://doi.org/10.3390/ma9050333

APA Style

Fan, Q., Chai, C., Wei, Q., & Yang, Y. (2016). The Mechanical and Electronic Properties of Carbon-Rich Silicon Carbide. Materials, 9(5), 333. https://doi.org/10.3390/ma9050333

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