Density functional theory study of the shallow boron impurity in $3C$-SiC and comparison with experimental data

In this paper, we present a detailed study of the boron impurity in $3C$-SiC (${\mathrm{B}}_{Si}$) in the cluster (CL) and supercell (SC) approximations, using representative local, gradient-corrected, and hybrid density functionals. Comparison of the theoretical spin-Hamiltonian parameters, calculated in the CL approximation using nonlocal density functionals, with the corresponding experimental values for the so-called shallow boron in SiC has proved that the latter is the ${\mathrm{B}}_{Si}^0$ defect. We analyze the motional effects in the electron paramagnetic resonance spectra, as well as the site dependence of the symmetry and SH parameters of ${\mathrm{B}}_{Si}^0$. The dependencies of the calculated structural and energetic parameters on the size of the model space both for SC and CL methods are presented. The calculated relative formation energies and transition energy levels for the neutral ${\mathrm{B}}_{Si}$ and ${\mathrm{B}}_C$ centers reveal substantial finite-size effects. A simple extrapolation scheme indicates that the supercells with up to ${10}^5$ atoms are required to achieve the desired accuracy level of 0.1 eV. Calculations suggest that ${\mathrm{B}}_C$ impurity is a hyperdeep acceptor, which acts as the electron trap rather than increases the $p$-type conductivity.

Figure 1

Model of the boron impurity ${\mathrm{B}}_{Si}^0$ in SiC. B-${\mathrm{C}}_1$ is the elongated bond; B-${\mathrm{C}}_2$, B-${\mathrm{C}}_3$, and B-${\mathrm{C}}_4$ are equivalent shortened bonds.

Figure 2

Structural parameters of the ${\mathrm{B}}_{Si}^0$ center in $3C$-SiC, $R_L$ (open circles) and $R_S$ (closed circles), as functions of the model space size in the cluster (a) and supercell (b) methods, calculated with different density functionals. In all the calculations the basis set 6-31G(d) was employed.

Figure 3

Mulliken spin population on the on-axis carbon atom of ${\mathrm{B}}_{Si}^0$ in $3C$-SiC (atom ${\mathrm{C}}_1$ in Fig. 1), as a function of the model space size in the cluster (a) and supercell (b) calculations, performed with different density functionals. In all the calculations the basis set 6-31G(d) was employed.

Figure 4

Schematic view of two equivalent equilibrium structures of ${\mathrm{B}}_{Si}^0$ (${\text{C}}_{3V}$ symmetry), and the transition state between them ($C_{2V}$ symmetry). The arrows indicate the probable most energetically favorable path for the reorientation of the defect.

Figure 5

Calculated dependencies of the formation energy differences of the ${\mathrm{B}}_{Si}$ and ${\mathrm{B}}_C$ centers in neutral ($q=0$) and negative ($q=-1$) charge states on the supercell dimensions.

Figure 6

The supercell size dependence of the defect energy of ${\mathrm{B}}_{Si}^0$ relative to the energy of the $3\times 3\times 3$ supercell, determined at the B3LYP level of theory. The filled squares indicate the calculated values, and the solid line represents the size dependence fitted according to Eq. (15).

Figure 7

The supercell size dependence of the formation energy difference between the ${\mathrm{B}}_{Si}^0$ and ${\mathrm{B}}_C^0$ centers, calculated with different XC functionals. The filled squares indicate the calculated values, and the solid line represents the size dependence fitted according to Eq. (15)

Figure 8

The supercell size dependence of the $(0/-)$ transition level difference between the ${\mathrm{B}}_{Si}^0$ and ${\mathrm{B}}_C^0$ centers, calculated with different XC functionals. The filled squares indicate the calculated values, and the solid line represents the size-dependence fitted according to Eq. (15)