Method for the determination of the index of refraction of a transparent layer by ellipsometry

摘要

Method for the determination of the index of refraction of a transparent layer (2) which, mounted on a substrate (1) is applied, with the help of a ellipsometric method, with the following process steps:- it is a pair of the ellipsometric angle psi (ψ_A) and delta (δ_A) on the layer to be investigated, (2) in the case of a first, higher layer thickness is measured,- it is a pair of the ellipsometric angle psi (ψ_B) and delta (δ_B) on the layer to be investigated, (2) with the same angle of incidence (a) in the case of a second, lower layer thickness or an uncoated surface of the substrate (1) is measured,- from the four measured ellipsometric angles (ψ_A, Ψ_B, Δ_A, Δ_B) an intermediate value is$S=\frac{\text{tan}{\mathrm{\Psi }}_A\cdot \text{cos}{\Delta }_A-\text{tan}{\mathrm{\Psi }}_B\cdot \text{cos}{\Delta }_B}{{\text{tan}}^2{\mathrm{\Psi }}_A\cdot {\text{sin}}^2{\Delta }_A-{\text{tan}}^2{\mathrm{\Psi }}_B\cdot {\text{sin}}^2{\Delta }_B}$are calculated and- the refractive index n₂ of the substrate (1) is calculated according to the following formula:$n=\frac{1}{\sqrt{2}}\sqrt{\frac{\left(n_1^2+n_2^2\right)\frac{E_2}{E_1}-n_2^2\left(n_2^2-n_1^2\right)+\sqrt{{\left(\frac{E_2}{E_1}-n_2^2\right)}^2{\left(n_2^2-n_1^2\right)}^2+4{\left(n_1{n}_2\right)}^4}}{\frac{E_2}{E_1}+n_1^2}}$wherein$\frac{E_2}{E_1}=\frac{n_2^2\text{ cos}{\mathrm{\alpha }}_1}{\text{cos}{\mathrm{\alpha }}_2\cdot \text{cos}\left({\mathrm{\alpha }}_1-{\mathrm{\alpha }}_2\right)}\cdot \left(2S\frac{n_1}{n_2}\frac{{\text{sin}}^2{\mathrm{\alpha }}_1}{\text{cos}\left({\mathrm{\alpha }}_1-{\mathrm{\alpha }}_2\right)}+1\right)$andn="11"n₁ the refractive index of the ambient medium,n₂ the refractive index of the substrate (1),α₁ the angle of incidence of the light andα₂ = arcsin (sine α₁ × n₁/n₂) are.