Simple analysis of spot splitting due to diffraction at surfaces with atomic steps

Abstract

Probing surface morphology by diffraction techniques is well established, especially for atomic steps on bare surfaces or on adlayer covered surfaces. The diffuse scattering contains information about the terrace size distribution. The sharpness of this distribution determines the shape of the spot profiles. While one observes a single broad shoulder for broad distributions, the shoulder splits into satellites for sharp distributions. For sharp distributions the average terrace size determines mainly the satellite position while the half-width of the satellites is governed by the standard deviation of the distribution. For broad distributions the situation is vice versa. Generally the shoulder can be fitted very well by two satellites with Lorentzian shape so that one can easily obtain the two prominent parameters of the terrace size distribution (average terrace size and standard deviation) from the splitting of the shoulder and the half-widths of the satellites. Additionally, this model is extended to two-dimensional surfaces with step trains. For a single step train with fluctuating steps the diffraction pattern shows a weak diffuse shoulder besides the strong satellites due to the average step-step distance. This effect is also predicted for crossing step trains which mimic mounds on the surface. Therefore equivalent to the one-dimensional case, the average terrace size and the local slope of the surface can be analysed from the satellite position and their half-width.