Investigating the correlation between the Urbach energy and asymmetry parameter of the Raman mode in semiconductors

Abstract

A quantitative correlation between the Urbach energy $({E}_{u})$ and asymmetry parameter $q$ of Raman spectra has been derived. For this purpose, the effect of electronic disorder $(\ensuremath{\sim}{E}_{u})$ on the possible interference between the electronic continuum states and discrete phononic states is reinvestigated. The equation of the form $\frac{I}{{q}^{2}}\ensuremath{\propto}\ensuremath{\xi}{E}_{u}\ifmmode\pm\else\textpm\fi{}\ensuremath{\lambda}$ ($I$: intensity of phonon mode $;\phantom{\rule{0.28em}{0ex}}\ensuremath{\xi},\ensuremath{\lambda}:$ some material-dependent parameters) has been obtained and verified experimentally on different semiconductors. The experimental results reveal an offset which has been understood as intrinsic or disorder-induced contribution to electron-phonon interactions in the system. The obtained equations quantitatively explain the changes in the Raman line shape due to disorder induced by atomic substitutions, temperature, etc., and provide understanding of the superposition between electronic and phononic states and of electron-phonon coupling in semiconductors with disorder.