Linescan Lattice Microscopy: A Technique for the Accurate Measurement and Mapping of Lattice Spacing and Strain with Atomic Force Microscopy.

Lateral resolution and accuracy in scanning probe microscopies are limited by the nonideality of piezoelectric scanning elements due to phenomena including nonlinearity, hysteresis, and creep. By taking advantage of the well-established atomic-scale stick-slip phenomenon in contact-mode atomic force microscopy, we have developed a method for simultaneously indexing and measuring the spacing of surface atomic lattices using only Fourier analysis of unidirectional linescan data. The first step of the technique is to calibrate the X-piezo response using the stick-slip behavior itself. This permits lateral calibration to better than 1% error between 2.5 nm and 9 μm, without the use of calibration gratings. Lattice indexing and lattice constant determination are demonstrated in this way on the NaCl(001) crystal surface. After piezo calibration, lattice constant measurement on a natural bulk MoS2(0001) surface is demonstrated with better than 0.2% error. This is used to measure nonuniform thermal mismatch strain for chemical vapor deposition (CVD)-grown monolayer MoS2 as small as 0.5%. A spatial mapping technique for the lattice spacing is developed and demonstrated, with absolute accuracy better than 0.2% and relative accuracy better than 0.1%, within a map of 12.5 × 12.5 nm2 pixels using bulk highly oriented pyrolytic graphite (HOPG) and MoS2 as reference materials.