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

We analyze photoemission spectra for Ge obtained for photon energies 6.5h25 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, 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. © 1975 The American Physical Society.