Project Alchemy: Beyond the Single-Material Limit (Angie's Mixing Rule: A Universal Compositional Framework for Near-Zero Lattice Mismatch in GaN-on-Si Heteroepitaxy)

This paper presents Project Alchemy—the third publication in the Angelica research series—establishing Angie’s Mixing Rule as a universal compositional framework for achieving near-zero lattice mismatch in GaN-on-Si(111) heteroepitaxy. The central thesis is that no single rare-earth oxide can surpass Gd2O3’s 0.15% mismatch with Si(111) using conventional single-material approaches; however, solidsolution mixing of two or more sesquioxides—governed by Angie’s Mixing Rule—can achieve lattice mismatch values approaching zero, surpassing all known single-material candidates. Three pathways are presented and simulated: Path A employs Eu2O3 (mismatch ≈0%), the geometrically optimal single-material candidate; Path B employs the mixed compound (Pr2O3)0.5(Y2O3)0.5 (mismatch ≈0.09%), experimentally demonstrated to grow epitaxially on Si(111); Path C generalises to Digital Alloy stacking, enabling arbitrary lattice constant tuning to any target precision. Simulation results demonstrate that Path A achieves residual stress of 108.3 MPa (−90.2%), and Path B achieves 116.7MPa (−89.5%)—both exceeding Angelica’s 88.5% benchmark. All RF, power, and reliability targets are met or exceeded.