10. Appendix

Chapter 6
Ab initio calculations of the bulk dielectric response of semiconductors
Chapter 6 703
In the additional references to Chap. 2 we have already mentioned the possibility
of calculating fully ab initio the dielectric response (Â1 and Â2 vs. ˆ).
There was already in the 3rd edition (Fig. 6.55) an example of such calculations
for GaN, compared with experimental results. During the past decade
this topic has received considerable attention. Some examples have been listed
among the additional references to Chap. 2, such as the book: Time Dependent
Density Functional Theory, ed. by M. A. L. Marques et al.. Most extant
calculations, however, do not include spin-orbit interaction nor the effect of
electron-phonon interaction (i.e., the dependence on temperature and on isotopic
masses). Since much of the information on these two effects has been
obtained from optical measurements, we have added references to pertinent
recent articles in this chapter. We also take advantage of this update to include
references to ab initio calculations of the second-harmonic generation
at surfaces, and on the Burstein-Moss shift of the band gap with increasing
doping.
K. Nakamura, Y. Yoshimoto, R. Arita, S. Tsuneyuki, M. Imada: Optical Absorption
Study by ab initio downfolding approach: Application to GaAs,
Phys. Rev. B77, 195126/1–13 (2008).
L. E. Ramos, J. Paier, G. Kresse, F. Bechstedt: Optical Spectra of Si Nanocrystallites:
Bethe-Salpeter Approach Versus Time-Dependent Density Functional
Theory. Phys. Rev. B78, 195423/1–9 (2008).
A. Walsh, J. L. F. Da Silva, S. H. Wei: Origins of Band Gap Renormalization in
Degenerate Doped Semiconductors, Phys. Rev. B78, 075211/1–5 (2008)
M. Shishkin and G. Kresse: Self-Consistent GW Calculation for Semiconductors
and Insulators. Phys. Rev. B75, 235102/1–9 (2007).
O. Onida, L. Reining and A. Rubio: Electronic Excitations: Density-Functional
vs. Many-Body Green’s-function Approaches. Rev. Mod. Phys. 74, 601–659
(2002).
V. Olevano and L. Reining: Excitonic Effects on the Silicon Plasmon Resonance.
Phys. Rev. Lett. 86, 5962–5965 (2001).
B. S. Mendoza, M.Palummo, G. Onida, R. del Sole: Ab Initio Calculation of
Second Harmonic Generation at the silicon [100] surface. Phys. Rev. B63,
205406/1–6 (2001).
Dependence of bandgaps on Temperature and Isotopic Masses:
Electron-Phonon Interaction
Most calculations of Â(ˆ) available in the literature imply that they apply to
T 0. This is, however not correct: even at T=0 the electron-phonon interaction,
not included in the calculation, can significantly alter the corresponding
electronic states. This fact has already been mention in Problem 6.19, in con-