Daniel Franta, David Nečas, Lenka Zajíčková, Ivan Ohlídal
Dispersion model of two-phonon absorption: application to c-Si
Optical Materials Express 4 (2014) 1641-1656
A dispersion model describing two-phonon absorption is developed using several simplifications of the quasiparticle approach. The dielectric response is constructed from absorption bands corresponding to individual additive and subtractive combinations of phonon branches. The model also includes thermal effects, changes of the transition strength with temperature, originating in Bose-Einstein statistics, and the shift of phonon frequencies accompanying thermal expansion. The model is applied to the analysis of experimental data measured in the IR range on crystalline silicon. The modeled spectral dependencies of optical constants are capable of describing all features in the transmittance spectra 70-1000 cm-1 observable at 300 K for float-zone silicon. The phonon frequencies in the points of symmetry are obtained independently in good agreement with ab initio calculations. The model of thermal effects is verified using ellipsometric measurements 300-1000 cm-1 in the temperature range of 300-500 K. The agreement between the modeled and experimental data is good, except for the spectral range 750-850 cm-1, in which a better agreement at temperatures above 300 K would require including the three-phonon absorption. The analysis provides a reliable value of the thermal coefficient describing the phonon frequency shift and proves that changes of structure broadening with temperature are negligible within the temperature range of 300-500 K.
DOI: 10.1364/OME.4.001641
You can also contact one of the authors: franta@physics.muni.cz, yeti@physics.muni.cz, lenkaz@physics.muni.cz, ohlidal@physics.muni.cz