PNMS Case Study 7 — Semiconductor Bandgap Structure: Si, Ge, GaAs, GaN, InSb

Comparative analysis of five semiconductor materials (Si, Ge, GaAs, GaN, InSb) using the Property-Neutral Matrixscope projection operator. Three material properties — bandgap energy, electron effective mass, and lattice constant — are projected into Planck-referenced signature space and evaluated using structural distance analysis. The study determines whether material separation is a uniform scale shift or a structural deformation. Results show that semiconductor separation is a multi-axis deformation dominated by electronic properties (bandgap energy and effective mass), while lattice geometry contributes weakly to structural distance.