10. Appendix

694 Appendix D
Chapter 3
Ab initio phonon calculations
The discussion of phonon dispersion relations in Chap. 3 was based on semiempirical
models of the force constants. In Fig. 3.3, however, an example of
ab initio calculations was shown for the dispersion relations of GaN. These
results are based on the total energy calculations obtained from an ab initio
electronic band structure. The atomic positions are then perturbed and
the corresponding changes in the total energy are used to obtain restoring
forces. This can be done either by using static atomic displacements (i.e.
time independent phonon eigenvectors), which correspond to frozen phonons,
or by energy functional perturbation theory. During the past decade several
of the ab initio computer codes mentioned in the update to the references
of Chap. 2, (e.g. ABINIT, CASTEP, VASP) and others (MedeA is the
name of a software platform which works with VASP for the computation
of materials properties including phonons. Further details can be found at
the URL:www.materialsdesign.com/), have been expanded so as to allow the
calculation of phonon dispersion relations. In the references that follow, the
reader will find examples of ab initio calculations of the lattice dynamics of
semiconductors. Whenever standard codes were used in these calculations, the
corresponding acronyms are given in red.
S. Baroni, S. de Gironcoli, A. del Corso, P. Giannozzi: Phonons and Related
Crystal Properties from Density-Functional Perturbation Theory. Rev. Mod.
Phys 73, 515–562 (2001).
M. D. Segall, P. J. D. Lindan, M. J. Probert, C. J. Pickard, P. J. Hasnip, S. J.
Clark and M. C. Payne: First-principles simulation: ideas, illustrations and the
CASTEP code. J. Phys.: Condens. Matter 14, 2717–2744 (2002).
X. C. Gonze: A Brief Introduction to the ABINIT software package. Z. für
Kristallographie, 220, 558–562 (2005).
S. J. Clark, M. D. Segall, C. J. Pickard, P. J. Hasnip, M. I. J. Probert, K. Refson
and M. C. Payne: First Principles Methods Using CASTEP. Z. für Kristallographie
220, 567–570 (2005).
K. Parlinski: First-Principle Lattice dynamics and Thermodynamics of Crystals.
J. Physics: Conference Series 92, 012009-012013 (2007). (VASP) (In this article
references to calculations for a number of semiconductors such as BN, GaN,
HgSe, ZnTe, AgGaS2 etc. can be found.)
A. H. Romero, M. Cardona, R. K. Kremer, R. Lauck, G. Siegle, J. Serrano,
X. C. Gonze: Lattice Properties of PbX (X=S, Se, Te): Experimental studies
and ab initio calculations including spin-orbit effects. Phys. Rev. B78,
224302–224310 (2008). (ABINIT) (In this work, evidence for the influence
of electronic spin-orbit coupling on the lattice dynamics and related properties
is presented.)