Thermal roughness of the homogeneous and inhomogeneous Cu(311) surface studied by high-resolution low-energy electron diffraction

The influence of temperature on the morphology of both the homogeneous and the inhomogeneous Cu(311) surfaces is investigated by high-resolution low-energy electron diffraction. Analyzing the spot profile of the diffracted electron beam under various scattering conditions provides information about both the surface roughness and inhomogeneities as a function of temperature. From the reversible spot broadening under the out-of-phase condition, it is concluded that atomic steps may be created reversibly on the Cu(311) surface by increasing the temperature. The critical temperature, at which the surface goes from the smooth, low-temperature phase into the rough, high-temperature phase, is obtained from the vanishing of the central spike of the (00) spot at ${\mathit{T}}_{\mathit{R}}$=750 K. On the basis of a detailed analysis of the spot profile, we find that the height-height correlation of the Cu(311) surface cannot be described by the logarithmic behavior predicted for Kosterlitz-Thouless roughening. Instead of this behavior, in the low-temperature phase the height-height correlation saturates exponentially as the lateral distance goes to infinity, while it is characterized by a linear divergence for the high-temperature phase. Sulfur segregated at the surface has two effects: Large areas of the Cu(311) surface become amorphous and the step-atom density increases. The surface is still rough at room temperature even with small amounts of sulfur. With increasing sulfur coverage, the roughness due to inhomogeneities overwhelms the thermally induced surface roughness.