An error-function compositional grading scheme in vertical-cavity surface-emitting lasers

An error-function analytical expression describing compositional grading in a 850 nm AlGaAs/GaAs top-emitting oxide confined vertical cavity surface emitting laser has been derived. Results are presented showing that the optical properties of the considered device utilizing the proposed error-function compositional scheme are superior over other grading schemes found in the literature. The advantages of the presented scheme over other schemes lies in its ability and flexibility of controlling the degree of grading unlike the other schemes reported in the literature were the grading profile is dependent on the grading function used.