Valence-band energy-momentum densities of amorphousSiO2by(e,2e)spectroscopy

We have measured the energy-momentum density of amorphous silicon dioxide using an $\mathrm{}(e,2e)\mathrm{}$ spectrometer with 20.8 keV incident, 19.6 keV scattered, and 1.2-keV ejected electron energies. The amorphous ${\mathrm{SiO}}_2$ sample was prepared by oxidizing a thin silicon membrane. The experimental data show a valence electronic structure characteristic of upper $p$-like and lower $s$-like bands. The width of the upper valence band is 10 eV. This is separated by 9 eV from the lower valence band, which exhibits 2-eV dispersion. We have calculated the energy-momentum density of α-quartz using the ab initio linear muffin-tin orbital method and the result is spherically averaged over all crystal directions to enable comparison with the experiment. The calculated electron momentum densities show very good agreement with experiment for both the upper and lower valence bands. The theoretical prediction of the energy separation between the upper and lower valence bands is about 2 eV smaller than that measured and this discrepancy is discussed. The agreement between theory and experiment suggests that the short-range order in silicon dioxide plays an important role in determining the electronic structure of this material.