Ellipsometry
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 Ep and Es 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-Tc 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-Tc 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 Tc [3,5,7]. Finally we have performed
measurements of the isotope shift of the IR-active phonon modes in the compound
YBa2Cu3O7-δ [13].
References
- C. Bernhard, T. Holden, A. Golnik, C.T. Lin and M. Cardona, "Far-infrared
c-axis conductivity of flux-grown
Y1-xPrxBa2Cu3O7
single crystals studied by spectral ellipsometry", accepted for publication in
Phys. Rev. B.
- 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).
- 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
YBa2Cu3O7-δ single
crystals revisited with ellipsometric measurements", Phys. Rev. B
61 618 (2000).
- 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).
- 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 YBa2Cu3Oy,"
Phys. Stat. Sol. (b) 215, 557 (1999).
- C.T. Lin and C. Bernhard, "Electrical Transport and Magnetic Properties of
Single Crystals of the Colossal Magnetoresistance (CMR) Manganite System
RE0.67Sr0.01Pb0.32MnO3,
RE=(Nd,Pr,La)", Phys. Stat. Sol. (b) 215, 685 (1999).
- 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).
- 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
Y1-xCaxBa2Cu3O7-δ
crystals", Physica C 317-318, 276 (1999).
- 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
Y1-xCaxBa2Cu3O7-δ
crystals", Phys. Rev. B. 59, R6631 (1999).
- 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).
- C. Bernhard, R. Henn, A. Wittlin, M. Kläser, G. Müller-Vogt, C.T. Lin, and
M. Cardona, "Electronic c-axis Response of
Y1-xCaxBa2Cu3O7-δ
Crystals Studied by Far-Infrared Ellipsometry", Phys. Rev. Lett.
80 1762 (1998).
- R. Henn, C. Bernhard, A. Wittlin, M. Cardona, and S. Uchida, "Far Infrared
Ellipsometry using Synchrotron Radiation: the out-of plane response of
La2-xSrxCuO4", Thin Solid
Films 313-314, 643 (1998).
- 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).
- 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).
contributed by Christian Bernhard and Todd Holden