Optical properties of intermixed vertical cavity surface emitting lasers: a theoretical model

摘要

The effect of intermixing on some important optical properties of vertical cavity surface emitting lasers (VCSELs) has been successfully modeled and analyzed. A combined superposition of the error function solution to the diffusion equation for a hypothetical Al_xGa_(1-x)As/GaAs VCSEL structure has been applied to simulate the intermixing process during growth or post-growth thermal annealing using a depth-independent and/or a depth-dependent interdiffusion coefficient. The simulations of the VCSEL reflectivity and phase shift revealed no appreciable difference between the two assumptions. It has been shown that for diffusion lengths of about 20 nm the overall VCSEL reflectivity and phase shift does not change significantly, however, the VCSEL bandwidth was shown to decrease at relatively small diffusion length. The width of the transmission "dip", which is the VCSEL emission wavelength was also shown to increase with increasing diffusion length indicating an appreciable intermixing of the active region and hence different conduction and valence band transitions due to modifications in the quantum wells and barriers shapes and widths. The presented model may provide a simple yet versatile technique for the analysis of interdiffusion during VCSEL growth or post-growth thermal annealing for device efficiency and optimization.