Influence of Bi-related impurity states on the bandgap and spin–orbit splitting energy of dilute III–V-Bi alloys: InP1−xBix, InAs1−xBix, InSb1−xBix and GaSb1−xBix

Abstract

Valence Band Anticrossing (VBAC) Model is used to calculate the changes in band structure of Bi containing alloys such as InP1−xBix, InAs1−xBix, InSb1−xBix and GaSb1−xBix due to the incorporation of dilute concentrations of bismuth. The coupling parameter CBi which gives the magnitude of interaction of Bi impurity states with the LH, HH and SO sub bands in VBAC depends on the increase in the HH/LH related energy level EHH/LH+, location of the Bi related impurity level EBi and valence band offset ΔEVBM between the endpoint compounds in the corresponding III–V-Bi. The reduction in band gap as well as the enhancement of the spin–orbit splitting energy is well explained using this model and the calculated results are compared with the results of Virtual Crystal Approximation (VCA) and Density Functional Theory (DFT) calculations, as well as with the available experimental data and are found to have good agreement. The incorporation of Bi mainly perturbs the valence band due to the interaction of the Bi impurity states with the HH, LH and SO bands. The lowering of the conduction band minimum (CBM) due to VCA is added with the upward movement of the HH/LH bands to get the total reduction in band gap for the bismides. The valence band shifts of 31.9, 32.5, 20.8 and 12.4 meV/at%Bi for InP1−xBix, InAs1−xBix, InSb1−xBix and GaSb1−xBix respectively constitute 65, 76, 59 and 31% of the total band gap reduction and the rest is the contribution of the conduction band shift. The spin–orbit splitting energy also shows significant increase with the maximum change in InPBi and the minimum in InSbBi. The same is true for Ga containing bismides if we make a comparison with the available values for GaAsBi and GaPBi with that of GaSbBi. It has also been observed that the increase in splitting energy is greater in case of the bismides such as InAsBi, InPBi and GaAsBi than the bismides such as InSbBi and GaSbBi with the parent substrates having higher values of splitting energy. This may be due to the proximity of the Bi related impurity level EBi with the SO bands of InAs, InP and GaAs.