Modelling the contribution of point defects to the Raman spectrum of crystalline materials
Résumé
Raman spectroscopy is a widely used tool for the characterization of
insulating or semiconducting materials of various kinds. The Raman shift is related
to vibrationals modes of the probed sample and, as such, can be related to the
atomic scale structure of the materials. However, when Raman spectrometry is used
to probe materials featuring disorder, radiation damage or simply a large enough
concentration of point defects, the relationship between the spectrum and the atomic
structure cannot be easily unraveled. In this paper we present a method to extend
the scale of the ab initio calculation of first order Raman spectra, based on Density
Functional Perturbation Theory (DFPT), to cope with larger systems, in order to
be able to describe point defects in the limit of low concentration. The goal is to
provide a quantitative basis for the interpretation of experimental Raman spectra.
The procedure consists in embedding force constants matrices, Born effective charges,
and Raman tensor, calculated with DFPT for a supercell with a point defect, into
a corresponding perfect bulk matrix to simulate a larger system. After describing
in detail the procedure, we present benchmark applications to three quite different
materials, containing defects of various kinds: silicon carbide with an intrinsic defect
(a carbon antisite), boron carbide with helium impurities |also in combination with
vacancies|, and caesium lead iodide with two different alloying impurities. Strengths
and limitations of the approach are discussed in the light of the three examples.