Photoemission spectroscopy using synchrotron radiation. II. The electronic structure of germanium

We analyze photoemission spectra for Ge obtained for photon energies $6.5\le h\nu \le 25$ eV and determine the position of energy bands at symmetry points for both filled and empty bands within 1 Ry of the gap. This experimental band structure is obtained using a recently developed anisotropic direct-transition model of photoemission applicable to cleaved single-crystal semiconductors. For the band-structure determination we also employ a direct transition analysis of optical spectra obtained by others. We fit nonlocal-pseudopotential calculations to the experimentally-determined band positions, and thereby determine the importance of both energy and $l=2\mathrm{}$, angular momentum nonlocality in the pseudopotential. Our results for the position of highlying conduction-band states suggest 0 to + 10% self-energy (exchange-correlation) corrections to the energy of electrons excited into the conduction bands. Energy bands which provide a good fit to the experimental band positions are used, along with pseudo-wave-function matrix elements, to calculate various physical properties (photoemission spectra, optical-response functions, and one-electron state densities), and the results of these calculations are compared with experiment. The quality of the fits obtained indicates that the electronic excited-state (and ground-state) properties of Ge for excitations far from the gap are described well by a one-electron model.