Absorption tail analysis by spectroscopic ellipsometry: a reduced-parameter approach to electric field...

We present a spectroscopic ellipsometry-based optical method for non-invasive, in situ electric field characterization via the absorption tail. The key advance is a reduction of the fitting problem from multiple free parameters to the reduced parameter by exploiting the intrinsic equivalence between the broadening factor γ and the space-charge region width L: for sufficiently large L (>90 nm), γ converges to zero. Unlike conventional Franz-Keldysh (FK) oscillation methods that require modulation spectroscopy and are restricted to wide, uniform fields, the absorption tail analyzed here persists under all field configurations-narrow or wide, uniform or non-uniform-making the approach universally applicable. Validated on three Si-doped GaN single crystals spanning carrier densities from 1.40 × 10¹⁷ to 3.20 × 10¹⁸ cm^-3, the method achieves a reduction in root mean square error up to 68.7%±41.2% compared to traditional multi-parameter approaches via Raman, KPFM, and ellipsometry. Requiring only standard broadband ellipsometry, the method is material-general and inherently compatible with external optical, electrical, and magnetic stimuli, establishing a practical platform for in situ optical field diagnostics in semiconductor and photonic devices.