Grazing-incidence x-ray-scattering study of step-step correlations on Si(001) surfaces

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Abstract
In this work, x-ray scattering was used to study regularly spaced steps on Si(001) surfaces. Staircases of steps were obtained after molecular-beam epitaxy of silicon onto atomically flat Si(001) surfaces with a small residual miscut (∼0.05°), and subsequent annealing at high temperature. Crystal-truncation-rod intensities are shown to be strongly affected by the macroscopic miscut. Detailed statistical information, such as the average terrace width and terrace-width disorder, were derived by analysis of the truncation-rod intensity distribution. The excellent resolution of the synchrotron experiment enabled us to show that, in some cases, the width of the diffraction peaks is very small, which is shown to arise from long-range correlations between successive terrace widths. A simple model is derived to analyze the peak intensity distribution without relying on the common assumption of statistical independence between neighboring terrace widths. By comparison with an unannealed sample, we show that annealing at high temperature favors the step ordering.