Physics-Informed Exponential Framework for Predicting Ge Incorporation during SiGe Selective Epitaxy in Nanoscale Trenches

High-germanium-content silicon–germanium (SiGe) selective epitaxial growth (SEG) plays a critical role in strain engineering for advanced gate-all-around (GAA) transistors. However, predictive process optimization remains challenging because the quantitative relationship between process parameters and Ge incorporation in confined nanoscale geometries is not yet fully understood. In this work, a physics-informed exponential framework is developed to quantitatively correlate SEG process parameters with Ge incorporation kinetics in nanoscale trenches. The proposed framework incorporates Arrhenius-type growth kinetics, surface-diffusion-limited transport, strain-gradient effects, and HCl-mediated competitive adsorption and etching mechanisms. Model parameters were extracted using nonlinear least-squares fitting and exhibited excellent agreement with experimental observations, with coefficients of determination ( R 2 ) exceeding 0.99 and average relative errors below 1%. Using the optimized process window predicted by the framework, void-free bottom-up filling was achieved in trenches approximately 60 nm wide with an aspect ratio of approximately 3:1. The optimized process yielded a maximum Ge content of 57.93 at. % while maintaining 100% selectivity against SiN and SiO 2 dielectric surfaces. Cross-sectional transmission electron microscopy (TEM), energy-dispersive X-ray spectroscopy (EDS), and X-ray diffraction (XRD) analyses revealed a graded Ge distribution that effectively reduced interfacial strain accumulation and defect formation. The framework should be regarded as a predictive engineering tool within the investigated process window rather than a mechanistic growth model. The results offer insights into selective epitaxial growth and may provide guidance for future source/drain engineering in advanced semiconductor technologies.