Comparison of electronic band structure and optical transparency conditions of InxGa1−xAs1−yNy∕GaAs quantum wells calculated by 10-band, 8-band, and 6-band k∙p models

Abstract

We have investigated the electronic band structure and optical transparency conditions of InxGa1−xAs1−yNy /GaAs quantum well (QW) using 10-band, 8-band and 6-band k·p models. The transition energy calculated by the 8-band model agrees very well with the values calculated by the 10-band model, especially in the range of high indium composition (35%) . Electron effective mass (me*) predicated by band anticrossing model, with nitrogen-related enhancement weakened as indium composition increases, was used in the 8-band model and was favored compared to the heavier value predicted by the phenomenological relationship. We have calculated the optical transition matrix element (Qincnv) using the Bloch wave functions for the k·p models and discovered that the inclusion of nitrogen-related energy level (EN) into the calculation of the conduction band by the 10-band k·p model yields lower differential gain (dG/dN) than that calculated by the 8-band k·p model on the same structure. Contrary to earlier reports that the reduction of dG/dN in InxGa1−xAs1−yNy /GaAs QW and thus the lower obtainable optical gain is due to the increase in me*, we have concluded that the reduction was due to the increased interaction between the IS> conduction-band state and ISN> nitrogen-related energy state, which weaken the optical transition matrix elements between valence band and conduction band. Our results also show that if me * is very large as predicted by the phenomenological model , dG/dN will increase monotonously with nitrogen composition. Moreover, neglecting valence band and conduction band interaction in k·p models will result in the prediction of higher dG/dN which is not accurate.