10. Appendix

Chapter 6 705
Strain-induced birefringence and intrinsic birefringence of cubic
semiconductors
Equation (6.158) describes the effect of an electric field on the dielectric function.
A similar tensor equation can be used to describe the effect of a tensorial
strain. Whereas a cubic crystal is usually assumed to be optically isotropic, a
finite wavevector q breaks this isotropy (p. 246 and Refs. [6.7, 8]). This effect
has recently received attention as determining the resolution of lenses used
for uv lithography. In the past few years ab initio calculations of strain induced
and q induced birefringence have been performed:
G. Bester, X. Wu, D. Vanderbilt and A. Zunger: Importance of Second order
Piezoelectric Effects in Zinc-Blende Semiconductors. Phys. Rev. Lett. 96,
187602–187605 (2006)
J. H. Burnett, Z. H Levine and E. L. Shirley: Photoelastic and Elastic Properties
of the Fluorite Structure Materials, LiF and Si. Phys. Rev. B68,
155120/1–12 (2003); erratum: Phys. Rev. B70, 239904 (2004).
J. H. Burnett, Z. H. Levine and E. L. Shirley: Intrinsic Birefringence in calcium
fluoride and barium fluoride. Phys. Rev. B64, 241102/1–4 (2001).
Optical Response of Semiconductor Surfaces
During the past decade many studies have concentrated on the optical response
of surfaces. This is due to advances in ab initio computational techniques
as well as development of highly sensitive experimental methods based
on ellipsometry and reflectometry. The results have proven to be useful for
the in situ characterization of epitaxial layers during growth.
The calculations are often performed on fictitious samples obtained by repetition
of thin layers so as to generate in the computer a three-dimensional
crystal. Many experiments are of the reflectance difference variety, which take
advantage of the fact that even on cubic crystals some surfaces (e.g. (110)) are
anisotropic. Recent theoretical and experimental references are as follows:
O. Pulci, O. Onida, R. del Sole and L. Reining: Ab Initio Calculation of Selfenergy
Effects on Optical Properties of GaAs(110). Phys. Rev. Lett. 81,
5374–5377 (1998).
P. Chiaradia, and R. del Sole: Difference-Reflectance Spectroscopy and
Reflectance-Anisotropy Spectroscopy on Semiconductor Surfaces. Surface
Review and Letters 6, 517–528 (1999).
W. G. Schmidt, F. Bechstedt, and J. Bernholc: Understanding Reflectance
Anisotropy: Surface-State Signatures and Bulk Related Features. J. Vac. Sci.
Technol. B18, 2215–2223 (2000).
W. G. Schmidt, N. Esser, A. M. Frisch, P. Vogl, J. Bernholc, F. Bechstedt, M.
Zorn, Th. Hannappel, S. Visbeck, F. Willig, and W. Richter: Understanding
Reflectance Anisotropy: Surface-State Signatures and Bulk-Related Features
in the Optical Spectrum of InP(001)(2×4). Phys. Rev. B61, R16335–8 (2000).