Electronic properties of InBixP1-x alloy in the P-rich range calculated using first-principles calculations

Abstract

First-principles calculations are carried out to explore the structural and electronic properties of the P-rich InBixP1-x versus bismuth fraction. It is found that the bowing coefficient for the lattice constant is minor (b=0.042 Å) due to the structural relaxation effect of the bond lengths in InBixP1-x. In the P-rich range, the InBixP1-x alloy has a direct bandgap. The result for the bond length shows that the average bond length in the InBixP1-x alloy becomes long with increasing bismuth fraction, resulting in weakening the total p−p coupling interaction and the total s−s coupling interaction. The descending of the conduction band minimum (CBM) is due to the weakened total p−p coupling interaction while the ascending of the valence band maximum (VBM) is owing to the weakened total s−s coupling interaction. Because of the descending of the CBM and the ascending of the VBM, the bandgap energy is shrunk. It is also found that the initial bismuth level is introduced below the VBM of InP due to the large strain of the In-Bi bond. In order to represent the bandgap energy in the P-rich range, the combination of a linear equation and the fusion-repelling model is proposed. It can offer an accurate description by setting V=1.39 eV2 and γ=1.61 eV. Besides, the positive formation energy shows that the Bi incorporation in InP is energetically unfavorable. This work is helpful for understanding the structural and electronic properties of the P-rich InBixP1-x alloy.