Far-Ultraviolet Reflectance Spectra and the Electronic Structure of Ionic Crystals

Abstract

The use of synchrotron radiation as a light source has made possible the measurement of the normal-incidence reflectance spectra of a number of ionic crystals in the photon energy range $6 \mathrm{eV}<\ensuremath{\hbar}\ensuremath{\omega}<36 \mathrm{eV}$ for temperatures $90\ifmmode^\circ\else\textdegree\fi{}\mathrm{K}<T<400\ifmmode^\circ\else\textdegree\fi{}\mathrm{K}$. The crystals investigated include KCl, KBr, RbCl, CsCl, CsBr, Ca${\mathrm{F}}_{2}$, Sr${\mathrm{F}}_{2}$, and Ba${\mathrm{F}}_{2}$. The spectra are compared and analyzed with particular reference to their dependence on temperature, chemical composition, and crystal structure. Special attention is given to the region of the spectra dominated by electronic excitation of the $p$ core levels which form the outer shell of the + ions. Sharp peaks (width \ensuremath{\le}0.2 eV) characterize the lower-energy portion of this region. They are correlated with the identity of the + ion and are assigned to transitions in the Brillouin zone using their observed temperature dependence and separation. The evidence is analyzed and found to favor the interpretation of these peaks as core excitons. At higher energies, there appear broader structures (width >0.5 eV) considered to be caused by interband transitions of core electrons. Because the crystals studied here encompass three different crystal structures, it is possible to correlate the shape of the core interband spectra with not only the crystal structure, but in fact with the nearest-neighbor coordination of the + ions. The broadening of valence- and conduction-band energies by lattice vibrations at elevated temperatures produces strong temperature dependence of interband as well as excitonic structures throughout the spectral region. The inherent sharpness of the optical structures in ionic crystals, which allows the temperature broadening to be observed, is attributed to the strong ionic character and localization of the crystal eigenstates, because these properties produce fairly sharp interband densities of states as well as excitons.