Charge-density oscillations onBe(101¯0): Screening in a non-free two-dimensional electron gas

The surface state on $\mathrm{Be}\left(101\mathrm{}¯0\right)$ has been investigated using a low-temperature scanning tunneling microscope (STM). The Fermi contour of this surface state is located at one boundary of the surface Brillouin zone, and surface-state electrons provide the main part of the charge density near the Fermi energy. $\mathrm{Be}\left(101\mathrm{}¯0\right),$ therefore, corresponds closely to a non-free two-dimensional electron gas. We have observed standing waves of the surface charge density on $\mathrm{Be}\left(101\mathrm{}¯0\right)$ near step edges and point defects. Such wave patterns derive from the interference of incoming and scattered electrons; they demonstrate the screening characteristics of the surface state. On $\mathrm{Be}\left(101\mathrm{}¯0\right)$ these waves were found to be highly anisotropic. It is shown that calculating the Fourier transforms of topographic STM images is a powerful method for determining the Fermi contour of the surface state. This method could even be applied to images that display a complex wave pattern arising from a random distribution of point scatterers. Fourier analysis also revealed that the charge density oscillations on $\mathrm{Be}\left(101\mathrm{}¯0\right)$ contain multiple periods that differ by reciprocal lattice vectors. These multiperiodic oscillations relate to the non-free character of the surface-state electrons and constitute an interference pattern of Bloch states. Fourier filtering was used to separate the charge-density oscillations from the topographic corrugation and to visualize their shape and spatial range. The experimental data are qualitatively discussed using a model calculation based on the scattering of Bloch electrons from planar obstacles in a two-dimensional conductor. Experimental results and model calculations highlight how the screening characteristics on $\mathrm{Be}\left(101\mathrm{}¯0\right)$ significantly deviate from the behavior expected for a free two-dimensional electron gas.