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

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. This work paves a way to overcome these obstacles using the period-dependent Fourier peaks suppression, which is invariant to affine distortions of the atomically resolved scanning probe microscopy images and to defects of the terrace atomic structure. We argue that the period of the triple-step arrays fabricated 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 intensities of the Fourier peaks in the differential maps, derived from raw topography images and containing stripes with the 7 times7 reconstruction, strongly depend on the period of the stripes. The suppression of the ninth Fourier peak indicates that the regular array of triple steps formed on the Si(5 5 7) wafers 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 [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 times7 unit cells.