Structural and electronic properties of silicon carbide

Introduction

Silicon carbide (SiC) is an important material used in a variety of industrial applications. SiC is known for its outstanding hardness, extreme strength and thermal conductivity which together with thermal expansion provides SiC with an excellent thermal shock resistance. Other key properties of this material are the superior chemical inertness and high elastic modulus. All together make SiC an excellent material for numerous high performance application under extreme operating conditions. It is used for example in abrasives, refractories, advanced ceramics, semiconductors, grinding wheels, and many other applications. SiC exists in over 250 crystalline forms with different structural and physical properties.
 
In this case study, we present DFT (density functional theory) calculations on structural and electronic properties of two major SiC polytypes. The calculations have been performed using the VASP[1] module of Scienomics MAPS platform[2] in collaboration with the Laboratoire de Chimie Théorique of the Sorbonne University. In the first part, the computational details including convergence studies are described. In the second part, we compare experimental and calculated properties of the silicon carbide polytypes 3C-SiC and 4H-SiC which are illustrated in Figure 1.
 

Figure 1: Unit cell of the silicon carbide polytypes 3C-SiC and 4H-SIC.
Figure 1: Unit cell of the silicon carbide polytypes 3C-SiC and 4H-SIC.

C-SiC has a cubic crystal lattice structure with a stacking sequence consisting of three layers ABC, while 4H-SiC has a hexagonal structure with a stacking sequence ABCB. Some properties like density or melting point are basically the same for both structures. However, other properties, especially electrical ones, can differ significantly depending on the polytype structure.
 
Computational details and convergence studies

The crystal structures of 3C-SiC and 4H-SiC were built with MAPS crystal builder taking the cell parameters from experimental results[3]. The calculations were performed using the hybrid density functional HSE06[4-6] together with PAW (Projector Augmented-Wave) potentials[7] as shipped with VASP. Best practices in the field of electronic structures calculations of solids typically require a careful selection of the energy cutoff and the k-point grid for the Brillouin zone. Therefore, the convergence of the total energy with respect to the energy cutoff and the k-point grid size was checked for 3C-SiC. The total energy of the primitive unit cell of 3C-SiC has been calculated and the energy cutoff and k-point grid, respectively, have been systematically increased.
 

Figure 2: Study of the convergence of the total energy as a function of the number of energy cutoff (a) and k-point grid (b).
Figure 2: Study of the convergence of the total energy as a function of the number of energy cutoff (a) and k-point grid (b).

Figure 2 summarizes the results of the convergence study. In Figure 2a, the convergence of the total energy with respect to the energy cutoff is illustrated and Figure 2b shows the convergence behavior of the total energy with respect to the number of k-points. Convergence of the absolute energy better than 1 meV is reached for an energy cutoff of 18 eV and a 8x8x8 k-point mesh for Brillouin zone integration.
 
Structural and Electronic Properties
 

Figure 3: Band structure of 3C (a) and 4H (b) silicon carbide systems.
Figure 3: Band structure of 3C (a) and 4H (b) silicon carbide systems.

The structures of 3C-SiC and 4H-SiC were geometry optimized using a convergence of the forces to 0.05 eV.Å-1. Based on the convergence criteria obtained in the preceding convergence study, an energy cutoff of 18 eV and a 8x8x8 k-point grid have been applied. To validate the level of theory chosen, the cell parameters and density of the geometry optimized structure were compared to experimental results[3]. The results are summarized in Table 1. These structures were used for calculating the band structures displayed in Figure 3. Both band structure show an indirect band gap. For 3C-SiC the band gap is to be considered between Γ and X points whereas for 4H-SiC the band gap is to be considered between Γ and M points.
 

Table 1: Computed and experimental values of 3C and 4H SiC cell parameters, densities and band gaps.
Table 1: Computed and experimental values of 3C and 4H SiC cell parameters, densities and band gaps.

For 3C-Si a band gap of 2.48 eV was obtained which is 0.44 eV lower compared to the band gap of 4H-SiC. This trend in good agreement with the experimentally observed trend [3].
 
Conclusion

In this case study, we have presented a DFT study on structural and electric properties of two commercially important SiC polytypes, 3C-SiC and 4H-SiC. Structural parameters of the geometry optimized structures are in very good agreement with literature data. Furthermore, the band gaps of both polytypes are in line with the experimental trend.
 
References:

  1. http://cms.mpi.univie.ac.at/VASP/
  2. http://scienomics.com/
  3. http://www.ioffe.ru/SVA/NSM/Semicond/SiC
  4. Ming-Zhu, Huang and W. Y. Ching, Phys. Rev. B 1993, 47, 9449.
  5. M Marsman, J Paier, A Stroppa and G Kresse. J. Phys.: Condens. Matter 20 (2008) 064201.
  6. Yoon-Suk Kim, Kerstin Hummer and Georg Kresse, Phys. Rev. B 2009, 80, 035203.
  7. P. E. Blochl, Phys. Rev. B 1994, 50, 17953.