Thermoreflectance of LiF between 12 and 30 eV

Abstract

The thermoreflectance spectrum of LiF between 12 and 30 eV was measured and several of the structures interpreted. The absorption-edge region is interpreted in terms of a Wannier exciton series converging to the fundamental band gap ${\ensuremath{\Gamma}}_{15}\ensuremath{\rightarrow}{\ensuremath{\Gamma}}_{1}$. Structure associated directly with the band gap is not manifest, so the ${\ensuremath{\Gamma}}_{15}\ensuremath{-}{\ensuremath{\Gamma}}_{1}$ energy is determined indirectly to be 14.2 \ifmmode\pm\else\textpm\fi{} 0.2 eV. The $n=1$ exciton state generates the first strong structure in $\ensuremath{\Delta}\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\epsilon}}$ and we suggest that the exciton-phonon interaction, along with a central-cell correction, can give a significant contribution to its binding energy. Structures at higher energy have been associated with the interband transitions $L_{3}^{}{}_{}{}^{\ensuremath{'}}\ensuremath{\rightarrow}{L}_{1}$ and $L_{2}^{}{}_{}{}^{\ensuremath{'}}\ensuremath{\rightarrow}{L}_{1}$ between the crystal-field-split valence band at $L$ and the lower conduction band. The strong electron-hole interaction modifies the expected line shape and a hyperbolic exciton, associated with the transitions at $L$, may exist as an antiresonance in the continuum. A strong feature at 22.2 eV in $\ensuremath{\Delta}\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\epsilon}}$ is associated with excitonic transitions at $X$ involving the second $d$-like conduction band. The corresponding peak at 26.4 eV in $\ensuremath{\Delta}[\mathrm{Im}(\ensuremath{-}\frac{1}{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\epsilon}}})]$ overlaps the "valence-band" plasmon at 24.6 eV. No evidence for double excitations is found around 25 eV in either $\ensuremath{\Delta}\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\epsilon}}$ or $\ensuremath{\Delta}[\mathrm{Im}(\ensuremath{-}\frac{1}{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\epsilon}}})]$. The $\ensuremath{\Delta}[\mathrm{Im}(\ensuremath{-}\frac{1}{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\epsilon}}})]$ spectrum shows for the first time which structures in the energy-loss function are generated by longitudinal excitons and which by plasmons.