Refraction and diffraction of photoelectrons at the Ge(001) surface

High-resolution photoemission spectra for the Ge 3d core levels were measured as a function of the polar emission angle from the Ge(001) surface for k${\to }_{\mathrm{para}}$ along either the Ge[010] or the Ge[110] azimuth. The spectra were deconvolved to yield the separate contributions from the surface atomic layer and the bulk. Both sets of data show a general increasing trend for the surface contribution relative to the bulk contribution for increasing polar emission angle; superimposed on the increasing trend are small aperiodic oscillatory variations due to diffraction. The data were analyzed by ignoring diffraction. Refraction was found to be important; from a theoretical fit to the data, we obtained a value of 15 eV for the crystal inner potential relative to the vacuum level and a value of 7.2 Å for the electron escape depth at an electron kinetic energy of 37 eV.