Dynamic Modeling of Stress-Induced Defect Expansion in VCSELs

Many failures of semiconductor-based oxide confined vertical cavity surface emitting lasers (VCSELs) are closely related to the generation and expansion of defects in the device structure. However, existing research has predominantly focused on the static study of defect morphology, with little attention given to analyzing the dynamic process of defect expansion, which limited our ability to predict device random failures due to lack of understandings on defect generation and expansion. To address this issue, we present a macroscopic phenomenological evolution model that describes the dynamic expansion of defects in VCSELs, in which the expansion of defects is treated as an anisotropic lattice strain diffusion process. We further exploit a diffusion-limited aggregation (DLA) method in solving the diffusion equation, which describes the random propagation and aggregation of strain in the vicinity of highly strained areas, resulting in defect formation when the stress from accumulated strain surpasses the bonding force of the atoms in the lattice. Our simulation result manages to replicate the dendritic expansion morphology of defects, aligning with experimental observations very well. Our model also predicts an accelerated defect expansion process, which is again consistent with the experimental result. This model finds relevance in applications such as random failure prediction through device aging, burn-in condition setting in device screening, and device structural andor material design improvement for mitigating defect expansion.