1 Investigation of Optical Properties n, k … index of refraction and damping  1,  2 … polarization and absorption Problems: The penetration depth of light is usually very low (metals)  surface sensitive measurement Influences on measured optical properties of the material: State of oxidation, distortion, adsorption and etc.

2 Problem with Complex Parameters >>> Solely the measurement of reflectivity is not sufficient <<< Solution: 1.The Kramers-Kronig analysis 2.Optical ellipsometry 3.Differential reflectometry

3 The Kramers-Kronig Analysis Relation between the real and imaginary part of a complex quantity Relation between the reflectivity (real part) and the phase shift (imaginary part)

4 The Kramers-Kronig Analysis Polarizability Ion resonance Electron resonance Frequency Microwave radiation Infrared radiation Ultraviolet radiation and x-rays Validity of Maxwell’s equations Dipole relaxation Measurement of reflectivity in a wide spectrum of wavelengths (measured in a broad frequency range)

5 Color Table E (eV) (nm) (eV)

6 Silver Reflectivity and permittivity from the Kramers-Kronig analysis The reflectivity for visible light is nearly one White light is reflected as white light Dispersion curve: Model of free and bound electrons can be applied

7 Copper Reflectivity and permittivity from the Kramers-Kronig analysis Reflectivity decreases for E > 2 eV ( < 620 nm) IR light has the best reflectivity For visible light the reflectivity is better for higher wavelengths  „red“ color of copper Dispersion curve as calculated from the model of free and bound electrons

8 Aluminum Reflectivity and permittivity from the Kramers-Kronig analysis Reflectivity is nearly constant (≈ 90%) for the whole spectrum of visible light White light is reflected as white light Dispersion curve: Model of free and bound electrons

9 Optical Ellipsometry Reflected light is always partially polarized Vacuum  Germanium: n=5,3

10 Optical Ellipsometry Incident light: a linear polarized wave  … angle of incidence Reflected light: an elliptical polarizes wave

11 Elliptical Polarization of a Propagating Wave  … phase shift of two linear polarized waves, which describes an elliptical polarized wave An elliptical polarized wave can be decomposed into two linear polarized waves.

12 Experimental Arrangement for Optical Ellipsometry

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14 Index of Refraction and Permittivity

15 Differential Reflectometry Comparative measurement for similar materials Investigation of differences in real structures (distortion, oxidation, composition, …)

16 Differential Reflectometry Investigation of “critical points” in the band structure

17 Alloys Cu-Zn alloy Change in color EDED

18 Change of Optical Properties Caused by Corrosion Oxidation of copper CuO 2 layer on the surface of copper Change in color