Band structure of silicon as measured in extended momentum space

Direct measurement of the wave function (or at least the modulus squared of the wave function, the spectral function) is an important goal in electron spectroscopy. This requires a state-selective (i.e., energy resolved) measurement of the momentum density in all of momentum space, not just the reduced Brillouin zone. Photoemission has been used very successfully to measure dispersion, mainly in the reduced zone scheme. Compton measurements determine a projection of the momentum density in the full momentum space, but do not contain energy information. Here we present electron momentum spectroscopy measurements of extremely thin silicon single crystals, that resolve both energy and momentum, not just the reduced momentum. Measurements were done along different lines in extended momentum space, that are equivalent within the reduced zone scheme. For different lines different bands dominate, resulting in dramatic different spectral momentum densities. The observed intensities compare well to the spectral function as obtained by linear muffin tin band structure calculations. The results show a unified picture that forms a bridge between Compton measurements determining densities and photoemission measurements determining dispersion.