Modeling and analysis of smoothly diffused vertical cavity surface emitting lasers

Inter-diffusion in a 850 nm AlGaAs/GaAs top-emitting oxide-confined vertical-cavity surface-emitting laser (VCSEL) has been modeled and analyzed. Some important VCSEL parameters such as, the threshold gain, relative confinement factor, and the effective cavity length have been derived as a function of diffusion length and were found to reliably describe intermixing in VCSELs. It has been shown that inter-diffusion in VCSELs during typical molecular beam epitaxy (MBE) and metal-organic vapor-phase deposition (MOCVD) growth conditions is negligible and has no effect on a various range of VCSEL parameters. The model reveled that the VCSEL reflectivity spectra remains roughly unchanged for diffusion lengths of up to 16 nm, however, it is associated with a very small resonance shift and a decrease in the band width. The VCSEL threshold gain was found to increase noticeably at small diffusion lengths. The error-function solution to the diffusion equation as presented in the model could be adapted as a new compositional grading scheme in VCSELs. This newly proposed compositional grading scheme could be controlled during VCSELs growth and/or by post-growth thermal treatment.