Interface and bulk effects in the attenuation of low-energy electrons throughCaF2thin films

We have studied for low kinetic electron energies the attenuation of the Si $2p$ core-level photoemission line through epitaxial ${\mathrm{CaF}}_2$ layers deposited on Si(111). Using an exponential attenuation model we have separated bulk and interface effects, which are, respectively, comprised within energy-dependent bulk attenuation length and interface transmission probability. The attenuation length has basically a constant value of $\sim$ 23 Å for kinetic energies above $\sim {\mathrm{E}}_F+15\mathrm{}\hspace{0.5em}\mathrm{eV},$ whereas the transmission probability has a maximum at $\sim$ 23 eV above $E_F.$ The latter effect is consistent with the presence of a large density of bulk ${\Lambda }_1$ states in the conduction band of ${\mathrm{CaF}}_2$ around 23.5 eV. Such a large density of states is obtained in a band calculation using the local-density approximation, and it is also detected in the background of secondaries of the photoemission spectra.