Steady progress in integrated circuit design has forced basic metrology to adopt silicon lattice parameter as a secondary realization of the SI meter that lacks convenient physical gauges for precise surface measurements at a nanoscale. To employ this fundamental shift in nanoscience and nanotechnology, we propose a set of self-organized silicon surface morphologies as a gauge for height measurements within the whole nanoscale (0.3-100 nm) range. Using 2 nm sharp atomic force microscopy (AFM) probes, we have measured the roughness of wide (up to 230 μm in diameter) singular terraces and the height of monatomic steps on the step-bunched and amphitheater-like Si(111) surfaces. For both types of self-organized surface morphology, the root-mean-square terrace roughness exceeds 70 pm but has a little effect on step height measurements having 10 pm accuracy for AFM technique in air. We implement a step-free 230-μm-wide singular terrace as a reference mirror in an optical interferometer to reduce the systematic error of height measurements from >5 nm to about 0.12 nm, which allows visualizing 136-pm-high monatomic steps on the Si(001) surface. Then, using a "pit-patterned" extremely wide terrace with dense but counted monatomic steps in a pit wall, we have optically measured mean Si(111) interplanar spacing (313.8 ± 0.4 pm) that agrees well with the most precise metrological data (313.56 pm). This opens up avenues for the creation of silicon-based height gauges using bottom-up approaches and advances optical interferometry among techniques for metrology-grade nanoscale height measurements.
Keywords: atomic force microscopy; height gauge; optical profilometry; silicon-based gauges; singular terraces; step height measurements.