10. Appendix

706 Appendix D
J. Pollmann, P. Kruger, A. Mazur, and M. Rohlfing: Electron, Phonon and Excitons
at Semiconductor Surfaces in Advances in Solid State Physics, Volume
42 (Springer, Berlin, Heidelbery, 2002) 189–206.
W. G. Schmidt, K. Seino, P. H. Hahn, F. Bechstedt, W. Lu, S. Wang, and J.
Bernholc: Calculation of Surface Optical Properties: from Qualitative Understanding
to Quantitative Predictions. Thin Solid Films, 455–456, 764–771
(2004).
P. Weightman, D. S. Martin, R. J. Cole, and T. Farrell: Reflection Anisotropy
Spectroscopy. Rep. Prog. Phys. 68, 1251–1341 (2005).
L. F. Lastras-Martínez, J. M. Flores-Camacho, A. Lastras-Martínez, R. E.
Balderas-Navarro and M.Cardona: Measurement of the Surface Strain Induced
by Reconstructed Surfaces of GaAs(001) using Photoreflectance and
Reflectance-Difference Spectroscopies. Phys. Rev. Letters 96, 047402–047405
(2006).
M. Marsili, O. Pulci, F. Fuchs, F. Bechstedt, and R. del Sole: Many Body Effects
in the Electronic and Optical Properties of the (111) Surface of Diamond.
Surface Science 601, 4097–4101 (2007).
K. F. Mak, M. Y. Sfeir, Y. Wu, C. H. Lui, J. A. Misewich, and T. F. Heinz: Measurement
of the Optical Conductivity of Graphene. Phys. Rev. Lett. 101,
196405–196408 (2008).
Dielectric Response due to Vibrational Excitations:
Born Effective Charges
The first order infrared absorption related to the excitation of phonons in polar
materials is discussed in Sect. 6.4. Its strength is related to the Born effective
charge e ∗ shown in Eq. (6.119). This effective charge has been calculated
for many semiconductors during the past 15 years using ab initio techniques.
e ∗ and other polarization related properties have been described by several
authors using the so-called Berry’s phase. Ab initio methods also allow the
calculation of the dependence of e ∗ on strain. Although a non-zero e ∗ is characteristic
of polar crystals and thus vanishes for crystalline Si, in amorphous
Si deviations from the regular lattice positions induce dynamic charges and,
consequently, ir absorption. Several references are listed as follows.
R. Resta: Macroscopic Polarization in Crystalline Dielectrics: the Geometric
Phase Approach. Rev. Mod. Physics 66, 899–915 (1994).
A. Debernardi, M. Bernasconi, M. Cardona, and M. Parrinello: Infrared Absorption
in Amorphous Silicon from ab initio Molecular Dynamics. Appl.
Phys. Lett. 71, 2692–2694 (1997).
X. Gonze and C. Y. Lee: Dynamical Matrices, Born Effective Charges, Dielectric
Permittivity Tensors, and Interatomic Force Constants from Density
Functional Theory. Phys. Rev. B55, 10355–10368 (1997).
F. Bernardini, V. Fiorentini, and D. Vanderbilt: Accurate Calculation of Polarization
Related Quantities in Semiconductors. Phys. Rev. B63, 193201/1–4
(2001).