Imaging empty states on the Ge(100) surface at 12 K

Abstract

Our understanding of bias-dependent scanning-tunneling-microscopy (STM) images is complicated not only by the multiplicity of the surface electronic structure, but also the manifold tunneling effects in probing semiconductor surfaces having directional dangling- and covalent-bond orbitals. Here we present a refined interpretation of empty-state STM images from the model semiconductor surface, Ge(100), on the basis of measurements at low temperature (12 K) combined with density-functional-theory calculations. In the lower-bias regime ($\ensuremath{\le}1.6\phantom{\rule{0.16em}{0ex}}\mathrm{V}$), the electron tunneling is found to occur predominantly in antibonding dangling-bond or/and dimer-bond states (${\ensuremath{\pi}}_{1}^{*},{\ensuremath{\pi}}_{2}^{*}$, and ${\ensuremath{\sigma}}^{*}$) of Ge(100) at the surface-parallel wave vector ${k}_{\ensuremath{\parallel}}=0$, leading to the tunneling current maxima located directly on the dimer rows. At higher biases (e.g., at 2 V), the current maxima are shifted to the position in the troughs between the dimer rows, because the tunneling occurs efficiently in the ${\ensuremath{\pi}}_{2}^{*}$ states at ${k}_{\ensuremath{\parallel}}\ensuremath{\ne}0$ associated with the dimer-up atoms of two adjacent dimer rows, i.e., because of increased sideways tunneling. Thus, the empty-state STM images of Ge(100), albeit strongly bias-dependent, reflect the dimer arrangement rather than the backbonds and surface resonances at all experimental conditions used. The results are also discussed in comparison with the counterpart system of Si(100).