Period-dependent suppression of Fourier peaks for topography images: Analysis of periodicity of triple-step arrays on vicinal Si(h h m) surfaces

Abstract

Reliable determination of the periodicity of multiatomic steps on high-Miller-index vicinal surfaces is often complicated by (i) the presence of relatively narrow terraces tilted at large angles relative to the scanning plane, and (ii) unavoidable distortions in the lateral direction resulting from creep and improper calibration of a piezo scanner. We argue that the period of the triple-step arrays on vicinal Si(5\,5\,6) and Si(5 5 7) single-crystal wafers can be determined from raw scanning tunneling microscopy data, without preliminary corrections, with precision approaching the interatomic distance. We demonstrate that the intensity of the Fourier peaks of the differential maps, derived from raw topography images by the difference-of-Gaussians approach, strongly depends on the period of the ordered triple-step arrays. This suppression of the ninth Fourier peak indicates that the regular array of triple steps has a period of $18b=5.99$ nm in projection onto the Si(1 1 1) terrace plane, where $b=0.333$ nm is the distance between atomic rows of the $1\times 1$ lattice in the $[\bar{1}\,\bar{1}\,2]$ direction. This means that the nominally (5\,5\,7)-oriented Si wafers may correspond locally to the Si(8 8 11) orientation. The method can be applied to the precise analysis of other vicinal surfaces with narrow and wide terraces containing an integer number of Si(1 1 1)$7\times 7$ unit cells.