Transfer-matrix modeling of spectral reflectivity for monitoring reactive-ion etching processes

We apply the transfer matrix method (TMM) to model the evolution of light spectral reflectivity during reactive ion etching of SiGe heterostructures used in electro-absorption modulators. The simulated reflectivity as a function of etch depth shows excellent agreement with in situ light spectral reflectometry measurements, enabling identification of wavelength ranges most sensitive to changes in the quantum-well (QW) stack. For Ge-rich SiGe (∼80% Ge), both modeling and experiment indicate a sensitivity window centered near 500 ± 50 nm, where the QW heterostructure exhibits a distinct spectral signature. We further show that introducing a thin SiGe etch-contrast layer (ECL) with ∼10% Ge concentration offset from the strain-relaxed buffer composition produces a clear reflectivity response that simplifies end point determination. These results demonstrate how TMM-assisted wavelength selection and ECL engineering can enhance the robustness of etch end point algorithms for advanced SiGe photonic device fabrication.