Influence of substrate absorption on the optical and geometrical characterization of thin dielectric films

Juan-María González-Leal, Rafael Prieto-Alcón, José-Andrés Angel, Dorian A. Minkov, and Emilio Márquez

Author Affiliations

Juan-María González-Leal, Rafael Prieto-Alcón, José-Andrés Angel, Dorian A. Minkov, and Emilio Márquez

^{}J. M. González-Leal (jmg62@cam.ac.uk) is with the Department of Chemistry, University of Cambridge, Lensfield Road, CB2 1EW, Cambridge, United Kingdom.

^{}R. Prieto-Alcón, J. A. Angel, and E. Márquez are with the Departamento de Física de la Materia Condensada, Facultad de Ciencias, Universidad de Cádiz, 11510 Puerto Real, Cádiz, Spain.

^{}D. A. Minkov is with the Fracture Research Institute, Department of Mechanical Engineering, Tohoku University, Aoba-ku, Sendai 980-8579, Japan.

Juan-María González-Leal, Rafael Prieto-Alcón, José-Andrés Angel, Dorian A. Minkov, and Emilio Márquez, "Influence of substrate absorption on the optical and geometrical characterization of thin dielectric films," Appl. Opt. 41, 7300-7308 (2002)

The role played by a glass substrate on the accurate determination of the optical constants and the thickness of a thin dielectric film deposited on it, when well-known envelope methods are used, is discussed. Analytical expressions for the two envelopes of the optical transmission spectra corresponding to films with both uniform and nonuniform thicknesses are derived, assuming the substrate to be a weakly absorbing layer. It is shown that accurate determination of the refractive index and the film thickness is notably improved when the absorption of the substrate is considered. The analytical expressions for the upper and lower envelopes are used to characterize optically and geometrically both uniform and nonuniform amorphous chalcogenide films. The results obtained are compared with those derived by use of expressions for the envelopes that neglect the substrate absorption. The comparison shows that overestimated refractive indexes and underestimated thicknesses are obtained when the conventional approach, in which the substrate absorption is neglected, is used.

Jonghoon Baek, Desiderio Kovar, John W. Keto, and Michael F. Becker Appl. Opt. 45(7) 1627-1639 (2006)

References

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λ_{tan}, wavelengths with tangent points; s and x_{
s
}, values of the refractive index and absorbance of the substrate at λ_{tan}, respectively; T_{+} and T_{-}, values of the upper and lower envelopes at λ_{tan}, respectively; n^{0}, estimated values for the refractive index obtained by solution of the system of Eqs. (13); m, order numbers for the tangent points; t, final values for the film thickness; n, final values for the refractive index at λ_{tan}; 〈t〉, average value of the thickness (of the t’s).
Bold data are values for the refractive index of the uncoated substrate, s [derived from its transmission spectrum and Eq. (5)] and final values for the refractive index, n, and for the film thickness, t. These are data obtained with the traditional approach in which the substrate absorption is neglected. Note that the final average value for the average value 〈t〉 = 1409 ± 7 nm (0.50%) is 〈t〉 = 1378 ± 33 nm (2.39%).

Table 2

Calculation of the Thickness and the Refractive Index of a Representative Nonuniform Filma

λ_{tan}, wavelengths with tangent points; s and x_{
s
}, values of the refractive index and absorbance of the substrate at λ_{tan}, respectively; T_{Δ+} and T_{Δ-}, values of the upper and lower envelopes at λ_{tan}, respectively; Δt, thickness variation; m, order numbers for the tangent points; n^{0}, estimated values for the refractive index obtained by solution of the system of Eqs. (14) after the determination of the thickness variation Δt; t̅, final values for the average film thickness; n, final values for the refractive index at λ_{tan}; 〈t̅〉, average value of the average film thickness (of the t’s).
Bold data are values for the refractive index of the uncoated substrate, s [derived from its transmission spectrum and Eq. (5)] and final values for the refractive index, n, and for the average film thickness, t̅. These are data obtained with the traditional approach in which the substrate absorption is neglected. Note that the final average value for the average value 〈t̅〉 = 2689 ± 15 nm (0.56%) is 〈t̅〉 = 2459 ± 32 nm (1.26%).

Tables (2)

Table 1

Calculation of the Thickness and the Refractive Index of a Representative Uniform Filma

λ_{tan}, wavelengths with tangent points; s and x_{
s
}, values of the refractive index and absorbance of the substrate at λ_{tan}, respectively; T_{+} and T_{-}, values of the upper and lower envelopes at λ_{tan}, respectively; n^{0}, estimated values for the refractive index obtained by solution of the system of Eqs. (13); m, order numbers for the tangent points; t, final values for the film thickness; n, final values for the refractive index at λ_{tan}; 〈t〉, average value of the thickness (of the t’s).
Bold data are values for the refractive index of the uncoated substrate, s [derived from its transmission spectrum and Eq. (5)] and final values for the refractive index, n, and for the film thickness, t. These are data obtained with the traditional approach in which the substrate absorption is neglected. Note that the final average value for the average value 〈t〉 = 1409 ± 7 nm (0.50%) is 〈t〉 = 1378 ± 33 nm (2.39%).

Table 2

Calculation of the Thickness and the Refractive Index of a Representative Nonuniform Filma

λ_{tan}, wavelengths with tangent points; s and x_{
s
}, values of the refractive index and absorbance of the substrate at λ_{tan}, respectively; T_{Δ+} and T_{Δ-}, values of the upper and lower envelopes at λ_{tan}, respectively; Δt, thickness variation; m, order numbers for the tangent points; n^{0}, estimated values for the refractive index obtained by solution of the system of Eqs. (14) after the determination of the thickness variation Δt; t̅, final values for the average film thickness; n, final values for the refractive index at λ_{tan}; 〈t̅〉, average value of the average film thickness (of the t’s).
Bold data are values for the refractive index of the uncoated substrate, s [derived from its transmission spectrum and Eq. (5)] and final values for the refractive index, n, and for the average film thickness, t̅. These are data obtained with the traditional approach in which the substrate absorption is neglected. Note that the final average value for the average value 〈t̅〉 = 2689 ± 15 nm (0.56%) is 〈t̅〉 = 2459 ± 32 nm (1.26%).