Ellipsometry is a technique which allows one to measure very accurately and with high reproducibility the complex dielectric function ε = ε₁ + i ε₂ of a given material. It measures the change in polarization of light upon non-normal reflection on the surface of a sample to be studied. A typical setup of an ellipsometry experiment is sketched in Fig.1. The incident light is linearly polarized with finite field components E_p and E_s in the directions parallel and perpendicular to the plane of incidence of the light (the index s originates from the German word senkrecht ). Upon reflection, the s- and p-components experience a different attenuation and phase shift according to the Fresnel equations (which are easily derived from Maxwell's equations of electrodynamics). The reflected light therefore is elliptically polarized giving the technique its name. The ellipse of polarization of the reflected light is then measured with a second polarizer (the so-called analyzer). The complex dielectric function epsilon can be obtained directly from the ellipticity of the reflected light simply by an inversion of the Fresnel-equations. Unlike conventional reflections techniques, ellipsometry requires no reference measurement and no extrapolation of the reflectivity towards zero and infinite energy. This makes the ellipsometry measurements more accurate and more reproducible than the conventional reflection measurements.

The technique of ellipsometry was invented by Paul Drude in 1887 who used it to determine the dielectric function of various metals and dielectrics. For 75 years following Drude's pioniering work only a handful of ellipsometric studies were done. In the late 1960's ellipsometry experienced a renaissance thanks to the availability of computers for numeric processing. It has since become one of the most important and powerful tools for the characterization of optical properties, in particular, of thin-film- and multi-layered materials. In the visible, NIR, and UV, this technique is particularly well suited to semiconductors and semiconductor based structures. Ellipsometers are widely applied in industry for characterization and on-line quality control.

More recently, the spectral range of the ellipsometric studies has been extended to the far-infrared regime. First attempts in this direction have been undertaken by Rösseler in the 1970's. The main experimental problem in the far-infrared spectral range is the absence of intense and brilliant light sources. We have circumvented this problem by making use of a synchrotron light source, which provides by about three orders of magnitude more brilliant light in the far-infrared as compared to conventionally available light sources, like mercury arc lamps.

From the dielectric function in the FIR-regime one can obtain valuable information about the low-energy charge excitations and the FIR-active (polar) phonons of a given material. Right now our interest is focuses on oxide based materials with unconventional electronic properties. Examples are the cuprate high-T_c superconductors [1,3-5,7-13], the colossal magneto-resistance (CMR) manganites [6], or thin films of ferroelectric SrTiO₃ [2].

The main part of our recent experimental work was done on cuprate high-T_c superconductors. In particular, we have investigated the formation of energy gaps in the superconducting and in the normal state electronic conductivity [1,4,8-12]. We also have performed extensive studies of the temperature dependence of some infrared-active phonon modes, which exhibit strong anomalies around T_c [3,5,7]. Finally we have performed measurements of the isotope shift of the IR-active phonon modes in the compound YBa₂Cu₃O_7-δ [13].
 

References

1. C. Bernhard, T. Holden, A. Golnik, C.T. Lin and M. Cardona, "Far-infrared c-axis conductivity of flux-grown Y_1-xPr_xBa₂Cu₃O₇ single crystals studied by spectral ellipsometry", accepted for publication in Phys. Rev. B.
    
2. A.A. Sirenko, C. Bernhard, A. Golnik, A.M. Clark, J. Hao, W. Si, and X.X. Xi, "Soft mode hardening in SrTiO₃ thin films, NATURE 404, 373-376 (2000).
    
3. C. Bernhard, D. Munzar, A. Golnik, C.T. Lin, A. Wittlin, J. Humlicek, and M. Cardona, "Anomaly of the oxygen bond-bending mode at 320 cm^-1 and additional absorption peak in c-axis infrared conductivity of underdoped YBa₂Cu₃O_7-δ single crystals revisited with ellipsometric measurements", Phys. Rev. B 61 618 (2000).
    
4. A. Golnik, C. Bernhard, J. Humlicek, M. Kläser, and M. Cardona, "The far-infrared in-plane conductivity of YBCO studied by ellipsometry", Phys. Stat. Sol. (b) 215, 553 (1999).
    
5. D. Munzar, C. Bernhard, A. Golnik, J. Humlicek, and M. Cardona, "A New Interpretation of the Phonon Anomalies in the Far-Infrared c-Axis Conductivity of Underdoped YBa₂Cu₃O_y," Phys. Stat. Sol. (b) 215, 557 (1999).
    
6. C.T. Lin and C. Bernhard, "Electrical Transport and Magnetic Properties of Single Crystals of the Colossal Magnetoresistance (CMR) Manganite System RE_0.67Sr_0.01Pb_0.32MnO₃, RE=(Nd,Pr,La)", Phys. Stat. Sol. (b) 215, 685 (1999).
    
7. D. Munzar, C. Bernhard, A. Golnik, J. Humlicek, and M. Cardona, "Anomalies of the infared-active phonons in underdoped YBCO as an evidence for the intra-bilayer Josephson effect", Solid State Commun. 122, 365 (1999).
    
8. C. Bernhard, D. Munzar, A. Wittlin, W. König, A. Golnik, C.T. Lin, M. Kläser, Th. Wolf, G. Müller-Vogt, and M. Cardona, "A far-infrared ellipsometric study of the spectral gap in the c-axis conductivity of Y_1-xCa_xBa₂Cu₃O_7-δ crystals", Physica C 317-318, 276 (1999).
    
9. C. Bernhard, D. Munzar, A. Wittlin, W. König, A. Golnik, C. T. Lin, M. Kläser, Th. Wolf, G. Müller-Vogt, and M. Cardona, "Far-infrared ellipsometric study of the spectral gap in the c-axis conductivity of Y_1-xCa_xBa₂Cu₃O_7-δ crystals", Phys. Rev. B. 59, R6631 (1999).
    
10. D. Munzar, C. Bernhard, and M. Cardona, "Does the peak in the magnetic susceptibility determine the in-plane infrared conductivity of YBCO? A theoretical study", Physica C 312, 121 (1999).
     
11. C. Bernhard, R. Henn, A. Wittlin, M. Kläser, G. Müller-Vogt, C.T. Lin, and M. Cardona, "Electronic c-axis Response of Y_1-xCa_xBa₂Cu₃O_7-δ Crystals Studied by Far-Infrared Ellipsometry", Phys. Rev. Lett. 80 1762 (1998).
     
12. R. Henn, C. Bernhard, A. Wittlin, M. Cardona, and S. Uchida, "Far Infrared Ellipsometry using Synchrotron Radiation: the out-of plane response of La_2-xSr_xCuO₄", Thin Solid Films 313-314, 643 (1998).
     
13. R. Henn, T. Strach, E. Schönherr, and M. Cardona, "Isotope effects in the optical phonons of YBa₂Cu₃O₇: eigenvector and infrared charge determination", Phys. Rev. B 55, 3285 (1997).
     
14. J. Kircher, R. Henn, M. Cardona, P.L. Richards, and G.P. Williams, "Far-infrared ellipsometry using synchrotron radiation", J. Opt. Soc. Am. B 104, 705 (1997).