Electric field induced bandgap enlargement of S- and N-hyperdoped silicon

In this paper, the effect of the electric field on the electronic structure of S-hyperdoped silicon and N-hyperdoped silicon is studied in detail by theory. The results show that the total bandgap initially increases and subsequently decreases with the increase of the electric field. Specifically, at an electric field of 0.1 V, the total bandgap reaches the maximum. With further increasing the electric field, the total bandgap decreases, but it is still larger than that in the absence of any electric field. The bandgap difference of the configuration in 2 × 2 × 2 supercell with and without electric field is approximately 0.2 eV. When 0.1 V of the electric field in the x and y directions is applied to the 2 × 2 × 3 supercell of the S- and N-hyperdoped silicon, the changes of the electronic structure are consistent. However, the band gap expansion is more obvious than that in the z direction electric field. While for 3 × 3 × 2 supercells of the S- and N-hyperdoped silicon, the band gap expansion is more significant under the z direction electric field than that under electric fields in the x and y directions. The difference in the bandgap variation under different directions of the electric field should be due to the direction-dependence of the impurity density in the 2 × 2 × 3 and 3 × 3 × 2 supercells. The results indicate that applying an electric field can further enlarge the bandgap of the S- and N-hyperdoped silicon and bring it closer to the optimal bandgap of an intermediate-band photovoltaic material.