Ellipsometry for Measurements at and below Monolayer Coverage

Ellipsometer, surface-tension, and contact-potential measurements were made simultaneously at and below monolayer coverage (θ = 1 to 0.05) on a clean mercury surface at room temperature. It has been demonstrated with molecules of known dimensions (caproic, lauric, stearic, behenic, and adamantane-carboxylic acids, and α bromonaphthalene and pentane) that the classical Drude equation for the relationship between the phase shift ( $\overline{\mathrm{\Delta }}$ − Δ) of reflected polarized light and the average effective film thickness d is valid below monolayer coverage. This is so even though the Drude equation was derived for thick films that are considered to be a continuum with index and density independent of thickness. The equation for the three-dimensional model is $\overline{\mathrm{\Delta }}$ − Δ = αd, where for less than monolayer coverage d is the hypothetical thickness the film would have if it were a continuum with index and density independent of d. The equation for the 3-D model remains valid below monolayer coverage, where the continuum property is not approximated, because the 2-D model gives essentially the same equation $\overline{\mathrm{\Delta }}$ − Δ = αd₀θ. In the 2-D model, the molecules are contained between the substrate surface and a plane d₀Å above the surface, where d₀ is the molecular diameter. The phase shift ( $\overline{\mathrm{\Delta }}$ − Δ) decreases as the fraction of the surface covered (θ) decreases because the index of refraction is a function of the surface density. Values of α, calculated with the bulk-liquid index of refraction (sodium D line) and the first-order Drude relation (for films with only a real part of the refractive index) can be used to calculate d (0.05d₀ to d₀) or θ (0.05 to 1) within a few percent with the equations above. The same values are obtained if the relationship between α and the film index (based on the 2-D model) is used to calculate α. The ellipsometer measurements indicate changes of orientation of the molecules on the surface. A technique is described for automatically recording ellipsometer measurements for very thin films (0–30 Å).