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Spatial Anisotropy of the Exciton Resonance in CaF 2 at 112 nm and its
Relation to Optical Anisotropy in the DUV
M. Richter, A. Gottwald
Physikalisch-Technische Bundesanstalt, Berlin, Germany
M. Letz
Schott Glas, Mainz, Germany
Abstract. Excimer lasers are widely used for industrial
applications such as photolithography of semiconductor
devices. The basic optical material for the excimer-laser
wavelengths in the deep ultraviolet is calcium fluoride
which shows an unexpected optical anisotropy at 157 nm.
In this context, we have measured the spatial anisotropy of
the exciton resonance at 112 nm by precision reflection
measurements using dispersed synchrotron radiation on
oriented samples of high purity. The results are discussed
in terms of the complex dynamic dielectric function and
explain the optical anisotropy by the interaction of
radiation with the cubic structure of a perfect crystal.
Introduction
Fluoride crystals are strongly ionic and have the largest
band gaps known for crystalline solids. As a consequence,
they are transparent even in the wavelength region of deep
ultraviolet (DUV) radiation and used for DUV optics.
Recently, the effect of an optical anisotropy for calcium
fluoride (CaF 2 ) has been observed at 157 nm which is of
great importance for DUV lithography (Burnett et al.
2001). Already the measured weak birefringence of ∆n/n ≈
10 -6 of the refractive index considerably influences the
design of imaging optics.
Due to its cubic symmetry, it is generally presumed that
the CaF 2 crystal shows isotropic optical properties.
However, strongly ionic crystals show deep excitonic
bound states. The most pronounced one in CaF 2 , the
Γ-exciton, is known to arise at 11.1 eV, yielding to a strong
and narrow absorption structure at a wavelength of about
112 nm. Close to such a strong absorption line, an optical
anisotropy can result from a slight deviation of the cubic
symmetry, due to the incident radiation field even at
optical wavelengths much larger than the lattice constant.
The effect of optical anisotropy in the vicinity of a narrow
absorption line was formulated by Ginzburg 1958. The
effect is well established at optical wavelengths and
usually called ‘spatial dispersion induced birefringence’.
In this work we describe a direct measurement of the
spatial anisotropy of the narrow absorption line at 112 nm
(Letz et al. 2003). The experiments were performed at the
UV and VUV beamline for detector calibration and
reflectometry in the Radiometry Laboratory of the
Physikalisch-Technische Bundesanstalt at the electron
storage ring BESSY II on extremely pure CaF 2 samples
with surface orientations in the (111) and (100) directions
of the crystals. The reflectance of the samples was
measured in a near-normal incidence geometry.
Results
The results of the reflection measurements are shown in
Fig. 1. When comparing the data of the two different
samples, a small but significant shift of about 0.2 nm
becomes apparent, the resonance structure of the sample
with (111) surface orientation being shifted towards
smaller wavelengths. To verify the experimental
significance of this small shift, the reproducibility of the
wavelength was tested by simultaneously recording
resonance absorption lines of Ar in a gas cell.
Figure 1. Experimental data (symbols) and fit (lines) of the
normal-incidence reflectance around the Γ-exciton of CaF 2 for a
(100) and (111) surface (Letz et al. 2003).
For interpreting our experimental data with regard to
exciton position and lifetime, we applied a least squares
fitting algorithm. The resulting fit curves are also shown in
Fig. 1. For the exciton positions one obtains for the
different crystal orientations:
(100): ηω 0 = 11.11(1) eV λ 0 = 111.6(7) nm
(111): ηω 0 = 11.13(1) eV λ 0 = 111.4(7) nm
Discussing the results in terms of the complex dynamic
dielectric function it can be demonstrated that the direction
of the shift for the exciton resonance as measured in the
present work is consistent with the sign of the optical
anisotropy as measured by Burnett et al. 2001 at 157 nm.
References
Burnett, J.H., Levine, Z.H., Shirley, E.L., Phys. Rev. B, 64,
241102R, 2001.
Ginzburg, V.L., JETP, 34, 1593, 1958.
Letz, M., Parthier, L., Gottwald, A., Richter, M., Phys. Rev. B, 67,
233101, 2003
Proceedings NEWRAD, 17-19 October 2005, Davos, Switzerland 145