Modeling threading dislocation density evolution in Ge/Si during cyclic annealing

A compact kinetic framework is developed to describe threading dislocation evolution in Ge/Si buffers by linking the final dislocation density to the initial defect level and an Arrhenius-weighted thermal budget that captures the combined effects of temperature, annealing time, and layer geometry. Despite extensive experimental progress in Ge-on-Si integration, optimization of growth and annealing parameters remains largely empirical, owing to the lack of a framework connecting processing conditions to defect evolution. Calibrated against electron channeling contrast imaging measurements from undoped and Sb-doped Ge/Si buffers with different annealing cycle counts, the model captures the overall reduction and saturation trends across the wafer set. This compact framework provides a practical means of assessing how initial defect density and accumulated thermal exposure influence final threading dislocation levels in thin Ge/Si buffers.