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Interpolation methods for phonon spectra in crystals
Author(s) -
Dresselhaus G.,
Dresselhaus M. S.
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560020734
Subject(s) - phonon , germanium , fourier transform , fourier series , physics , maxima and minima , spectral line , dispersion (optics) , condensed matter physics , computational physics , molecular physics , silicon , optics , quantum mechanics , mathematics , mathematical analysis , optoelectronics
Abstract The use of the Fourier expansion technique, which is based entirely on crystal symmetry, is studied by application of the technique to the phonon dispersion relations in silicon and germanium. In order to facilitate the convergence of the Fourier expansion, the interaction between the phonons and the low‐lying electronic excitations is explicitly considered in terms of a Fourier expansion of this interaction. In the present approach, which only treats short‐range forces, the simplest model which provides an adequate fit to the known experimental data utilizes nine adjustable parameters. By comparing certain tunneling and inelastic neutron scattering data, the location of the conduction band minima in germanium along the Δ axis is determined. The fractional distance to the X point for these minima is 0.82 ± 0.04.