  In this paper we describe a new variant of null ellipsometry to determine
thicknesses and optical properties of thin films on a substrate at cryogenic
temperatures. In the PCSA arrangement of ellipsometry the polarizer and the
compensator are placed before the substrate and the analyzer after it. Usually,
the polarizer and the analyzer are rotated to find the intensity minimum
searched for in null ellipsometry. In our variant we rotate the polarizer and
the compensator instead, both being placed in the incoming beam before the
substrate. Therefore the polarization analysis of the reflected beam can be
realized by an analyzer at fixed orientation. We developed this method for
investigations of thin cryogenic films inside a vacuum chamber, where the
analyzer and detector had to be placed inside the cold shield at a temperature
of T approx. 90K close to the substrate. All other optical components were
installed at the incoming beam line outside the vacuum chamber, including all
components which need to be rotated during the measurements. Our null
ellipsometry variant has been tested with condensed krypton films on a highly
oriented pyrolytic graphite substrate (HOPG) at a temperature of T approx. 25K.
We show that it is possible to determine the indices of refraction of condensed
krypton and of the HOPG substrate as well as thickness of krypton films with
reasonable accuracy.
