Use and Misuse of Optical Dispersion Formulas for the IR Index of Silicon

Interference measurements of the IR refractive index of silicon conflict with prism measurements by an order of magnitude more than their precision. This arises from erroneous use of classical dispersion formulas for polar optical glass to analyze measurement on homopolar silicon. We show that many of these dispersion formulas, often considered empirical, follow from the Kramers-Kronig (K-K) relations:1) Binomial expansion of the K-K integrand gives the index as a series of absorption-spectrum moments leading to the Cauchy, Briot and Conrady formulas; 2) Expansion of the absorption spectrum in delta-functions yields the Sellmeier, Drude-Ketteler and Hartmann expressions. In these formulas the contribution from electronic polarization is explicit, but phonon terms are often obscure. In two specific cases for silicon, confusion of electronic and phonon excitation energies in the Li-Sellmeier formula and misunderstanding of the Cauchy and Briot expansions in the Baumeister-Edwards analysis distorted the original data. The latter are now lost precluding reanalysis. Hence, we recommend use of prism data until new interference measurements are made.